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TD[(,)-293(the)-284(only)-283(p)-28(oin)27(t)-282(that)-284(is)-283(added)-283(b)26(y)-282(compactifying)-283(is)-284(the)-283(p)-28(oin)27(t)]TJ -108.21 -11.95 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(p)]TJ/F12 6.97 Tf 9.43 -1.5 TD[(2)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\).)-425(Consider)-278(the)-277(t)26(w)28(o)-276(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 116.14 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-277(and)]TJ/F5 9.96 Tf 25.45 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-277(where)]TJ/F5 9.96 Tf 34.88 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-277(=)]TJ/F5 9.96 Tf 17.15 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-110(+)]TJ/F5 9.96 Tf 13.82 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\(cos)]TJ/F5 9.96 Tf 18.87 0 TD[(\256)-3(;)]TJ/F3 9.96 Tf 10.83 0 TD[(sin)]TJ/F5 9.96 Tf 13.89 0 TD[(\256)]TJ/F3 9.96 Tf 6.41 0 TD[(\).)]TJ -356.1 -11.96 TD[(If)]TJ/F5 9.96 Tf 9.18 0 TD[(t)]TJ/F3 9.96 Tf 6.13 0 TD[(go)-28(es)-254(to)-255(zero,)]TJ/F5 9.96 Tf 55.72 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-254(will)-255(coincide)-254(with)]TJ/F5 9.96 Tf 83.74 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\).)-418(Describ)-27(e)-255(the)-255(V)83(oronoi)-254(diagram)-255(of)]TJ/F5 9.96 Tf 151.86 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\(0\))]TJ -350.01 -11.95 TD[(and)]TJ/F5 9.96 Tf 19.35 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\(0\))-330(as)-331(in)-331(Figure)-331(1.3.)-444(Then)-330(ev)26(ery)-330(distinct)-331(v)55(alue)-330(of)]TJ/F5 9.96 Tf 216.43 0 TD[(\256)]TJ/F3 9.96 Tf 9.7 0 TD[(corresp)-28(onds)-331(to)-331(a)-331(distinct)]TJ -254.96 -11.95 TD[(direction)-329(of)-329(the)-329(bisector)-329(of)-329(the)-329(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 165.31 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\(0\))-329(and)]TJ/F5 9.96 Tf 35.33 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\(0\).)-442(But)-329(this)-329(means)-329(that)-330(there)-329(is)]TJ -219.6 -11.95 TD[(not)-364(one)-365(V)82(oronoi)-363(diagram)-365(corresp)-27(onding)-365(to)]TJ/F5 9.96 Tf 189.89 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\(0\))-329(=)]TJ/F5 9.96 Tf 27.04 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\(0\))-364(but)-364(a)-365(complete)-365(collection)]TJ -235.89 -11.95 TD[(of)-333(diagrams,)-333(parameterized)-334(b)27(y)]TJ/F5 9.96 Tf 135.43 0 TD[(\256)]TJ/F3 9.96 Tf 9.73 0 TD[(mo)-27(d)-333(2)]TJ/F5 9.96 Tf 27.39 0 TD[(\274)]TJ/F3 9.96 Tf 6.03 0 TD[(.)]TJ/F1 11.95 Tf -178.58 -32.56 TD[(Compactifying)-375(using)-375(angles.)]TJ/F3 9.96 Tf 0 -22.06 TD[(By)-404(no)27(w,)-420(the)-404(atten)27(tiv)27(e)-402(reader)-404(should)-404(b)-28(e)-404(con)27(vinced)-403(that)-404(it)-403(is)-404(not)-404(a)-404(strange)-404(idea)-403(to)]TJ 0 -11.95 TD[(use)-342(angles)-342(for)-342(a)-343(suitable)-342(compacti\257cation.)-471(In)-342(Chapter)-342(5)-343(w)27(e)-341(ma)27(y)-342(consider)-342(all)-342(angles)]TJ 0 -11.96 TD[(b)-28(et)27(w)28(een)]TJ/F5 9.96 Tf 38.91 0 TD[(n)]TJ/F3 9.96 Tf 9.75 0 TD[(p)-28(oin)27(ts:)-535(w)27(e)-378(start)-378(with)]TJ/F5 9.96 Tf 97.31 0 TD[(n)]TJ/F3 9.96 Tf 9.75 0 TD[(distinct,)-390(lab)-27(eled)-379(p)-28(oin)27(ts)-378(in)-379(the)-379(plane.)-581(F)82(or)-378(ev)27(ery)]TJ -155.72 -11.95 TD[(t)27(w)28(o)-407(p)-27(oin)26(ts)]TJ/F5 9.96 Tf 50.23 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 7.37 1.49 TD[(and)]TJ/F5 9.96 Tf 20.11 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 8.25 1.49 TD[(with)]TJ/F5 9.96 Tf 23.43 0 TD[(i)-400(<)-402(j)]TJ/F3 9.96 Tf 27.9 0 TD[(w)28(e)-407(consider)-407(the)-408(directed)-407(line)]TJ/F5 9.96 Tf 131.34 0 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.49 TD[(ij)]TJ/F3 9.96 Tf 11.07 1.49 TD[(passing)-407(through)]TJ -292.69 -11.95 TD[(the)-401(t)27(w)28(o)-400(p)-27(oin)26(ts.)-645(This)-401(line)-401(mak)27(es)-400(some)-400(angle)]TJ/F5 9.96 Tf 198.94 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.49 TD[(ij)]TJ/F3 9.96 Tf 11.01 1.49 TD[(mo)-27(d)-401(2)]TJ/F5 9.96 Tf 28.06 0 TD[(\274)]TJ/F3 9.96 Tf 10.02 0 TD[(with)-400(the)-401(horizon)27(tal)-400(axis.)]TJ -254.4 -11.95 TD[(The)]TJ/F9 9.96 Tf 20.83 0 TD[(angle)-390(map)]TJ/F5 9.96 Tf 48.28 0 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.49 TD[(D)30(A)]TJ/F14 4.98 Tf 11.66 -1 TD[(n)]TJ/F3 9.96 Tf 9.06 2.49 TD[(maps)-368(a)-369(con\257guration)-369(of)]TJ/F5 9.96 Tf 107.46 0 TD[(n)]TJ/F3 9.96 Tf 9.65 0 TD[(distinct)-368(p)-28(oin)27(ts)-368(to)-369(the)]TJ/F15 9.96 Tf 96.69 8.07 TD[(\241)]TJ/F7 6.97 Tf 4.57 -3.65 TD[(n)]TJ/F12 6.97 Tf 0.48 -7.86 TD[(2)]TJ/F15 9.96 Tf 4.44 11.51 TD[(\242)]TJ/F3 9.96 Tf 8.24 -8.07 TD[(directed)]TJ -327.85 -11.95 TD[(angles)]TJ/F5 9.96 Tf 30.8 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.5 TD[(ij)]TJ/F3 9.96 Tf 11.19 1.5 TD[(with)]TJ/F5 9.96 Tf 23.55 0 TD[(i)-421(<)-421(j)]TJ/F3 9.96 Tf 24.24 0 TD[(.)-703(Let)]TJ/F5 9.96 Tf 28.47 0 TD[(T)]TJ/F3 9.96 Tf 11.39 0 TD[(b)-27(e)-419(a)-420(triangle)-419(with)-420(v)27(ertices)-419(1,)-441(2)-419(and)-420(3.)-703(If)-420(w)27(e)-418(kno)26(w)]TJ -136.01 -11.95 TD[(the)-477(angles)]TJ/F5 9.96 Tf 49.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(12)]TJ/F3 9.96 Tf 8.44 1.5 TD[(,)]TJ/F5 9.96 Tf 7.88 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(13)]TJ/F3 9.96 Tf 13.2 1.5 TD[(and)]TJ/F5 9.96 Tf 20.8 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(23)]TJ/F3 9.96 Tf 8.44 1.5 TD[(,)-513(w)27(e)-476(kno)26(w)-476(in)-478(fact)-477(the)-477(shap)-28(e)-478(of)-477(the)-478(triangle)]TJ/F5 9.96 Tf 202.92 0 TD[(T)]TJ/F3 9.96 Tf 7.21 0 TD[(.)-876(So,)]TJ/F5 9.96 Tf -337.96 -11.96 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.49 TD[(D)30(A)]TJ/F16 4.98 Tf 11.66 -1 TD[(3)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F6 9.96 Tf 3.87 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\))-309(describ)-28(es)-310(in)-310(a)-310(w)27(a)28(y)-309(all)-310(distinct)-309(triangles)-310(on)-310(three)-310(p)-28(oin)27(ts.)-435(W)82(e)-309(describ)-28(e)]TJ -59.79 -11.95 TD[(explicitly)-370(this)-370(image)]TJ/F5 9.96 Tf 92.46 0 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.49 TD[(D)30(A)]TJ/F16 4.98 Tf 11.66 -1 TD[(3)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F6 9.96 Tf 3.87 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\))-370(in)-370(Chapter)-370(5.)-556(W)83(e)-370(explain)-370(the)-370(consequences)-371(of)]TJ -152.25 -11.95 TD[(the)-415(action)-416(of)-416(the)-415(symmetric)-416(group)]TJ/F5 9.96 Tf 157.19 0 TD[(S)]TJ/F12 6.97 Tf 6.11 -1.49 TD[(3)]TJ/F3 9.96 Tf 8.61 1.49 TD[(on)-415(the)-416(lab)-27(els)-416(of)-415(the)-416(three)-416(v)27(ertices.)-690(Finally)]TJ -171.91 -11.95 TD[(w)27(e)-360(giv)27(e)-360(geometric)-361(in)27(terpretations)-360(of)-361(b)-28(oundary)-360(p)-28(oin)27(ts)-360(of)]TJ/F5 9.96 Tf 247.54 0 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.5 TD[(D)30(A)]TJ/F16 4.98 Tf 11.66 -0.99 TD[(3)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F6 9.96 Tf 3.87 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.5 TD[(3)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\))-360(in)-361(terms)-361(of)]TJ -307.33 -11.95 TD[(degenerate)-333(con\257gurations.)]TJ 0 -15.39 TD[(The)-407(\257rst)-408(compacti\257cation)-407(that)-408(w)27(e)-406(encoun)27(ter)-407(is)]TJ/F6 9.96 Tf 212.83 0 TD[(CD)27(A)]TJ/F7 6.97 Tf 22 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(,)-425(the)]TJ/F9 9.96 Tf 24.9 0 TD[(c)51(omp)51(acti\257c)51(ation)]TJ/F3 9.96 Tf 73.8 0 TD[(of)]TJ/F9 9.96 Tf 12.08 0 TD[(di-)]TJ -351.03 -11.95 TD[(r)50(e)51(cte)52(d)-435(angles)]TJ/F3 9.96 Tf 55.63 0 TD[(.)-698(This)-418(space)-419(is)-418(de\257ned)-418(as)-418(the)-418(closure)-418(of)-418(the)-418(graph)-419(of)-418(the)-418(angle)-418(map)]TJ/F5 9.96 Tf -55.63 -11.95 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.49 TD[(D)30(A)]TJ/F14 4.98 Tf 11.66 -1 TD[(n)]TJ/F3 9.96 Tf 5.38 2.49 TD[(,)-469(so)-442(a)-442(p)-28(oin)27(t)]TJ/F5 9.96 Tf 57.23 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.49 TD[(n)]TJ/F10 9.96 Tf 9.99 1.49 TD[(2)]TJ/F6 9.96 Tf 11.21 0 TD[(CD)27(A)]TJ/F7 6.97 Tf 21.99 -1.49 TD[(n)]TJ/F3 9.96 Tf 9.83 1.49 TD[(consists)-441(of)]TJ/F5 9.96 Tf 50.19 0 TD[(n)]TJ/F3 9.96 Tf 10.38 0 TD[(p)-28(oin)27(ts)-441(and)]TJ/F15 9.96 Tf 51.47 8.07 TD[(\241)]TJ/F7 6.97 Tf 4.57 -3.65 TD[(n)]TJ/F12 6.97 Tf 0.47 -7.85 TD[(2)]TJ/F15 9.96 Tf 4.45 11.5 TD[(\242)]TJ/F3 9.96 Tf 8.97 -8.07 TD[(angles)-441(b)-28(et)27(w)27(een)-441(those)]TJ -269.44 -11.95 TD[(p)-28(oin)27(ts.)-484(If)]TJ/F5 9.96 Tf 44.31 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.5 TD[(n)]TJ/F3 9.96 Tf 8.87 1.5 TD[(is)-346(a)-347(b)-28(oundary)-347(p)-28(oin)27(t)-346(of)]TJ/F6 9.96 Tf 101.19 0 TD[(CD)28(A)]TJ/F7 6.97 Tf 21.99 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(,)-350(then)-347(not)-347(all)-346(p)-28(oin)27(ts)-346(need)-347(to)-347(b)-28(e)-347(distinct.)]TJ -186.94 -11.95 TD[(In)-280(an)27(y)-279(case)-279(w)26(e)-279(kno)27(w)-279(for)-279(ev)26(ery)-278(t)26(w)28(o)-279(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 178.52 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.5 TD[(i)]TJ/F5 9.96 Tf 3.31 1.5 TD[(;)-166(p)]TJ/F7 6.97 Tf 9.44 -1.5 TD[(j)]TJ/F10 9.96 Tf 6.96 1.5 TD[(2)]TJ/F5 9.96 Tf 9.41 0 TD[(\260)]TJ/F7 6.97 Tf 5.15 -1.5 TD[(n)]TJ/F3 9.96 Tf 8.21 1.5 TD[(an)-280(angle)]TJ/F5 9.96 Tf 38.78 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.5 TD[(ij)]TJ/F3 9.96 Tf 9.8 1.5 TD[(and)-279(the)-280(p)-28(osition\(s\))]TJ/F5 9.96 Tf -280.97 -11.96 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F10 9.96 Tf 6.09 1.49 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 10.51 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 7.52 1.49 TD[(or)]TJ/F5 9.96 Tf 12.2 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 6.08 1.49 TD[(=)]TJ/F5 9.96 Tf 10.52 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.19 1.49 TD[(.)-444(This)-334(implies)-333(that)-333(for)]TJ/F5 9.96 Tf 100.57 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.49 TD[(n)]TJ/F3 9.96 Tf 8.74 1.49 TD[(a)-333(V)83(oronoi)-333(diagram)]TJ/F5 9.96 Tf 84.16 0 TD[(V)]TJ/F3 9.96 Tf 8.02 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(\260)]TJ/F7 6.97 Tf 5.15 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\))-333(is)-334(de\257ned.)]TJ -298.25 -15.38 TD[(In)-325(Chapter)-325(6)-325(w)27(e)-324(pro)27(v)28(e)-324(a)-325(con)26(tin)28(uit)28(y)-324(theorem)-325(for)-325(V)82(oronoi)-324(diagrams)-325(of)-325(data)-325(sets)-325(from)]TJ/F6 9.96 Tf 0 -11.95 TD[(CD)27(A)]TJ/F7 6.97 Tf 22 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(.)-493(It)-349(states)-350(essen)27(tially)-348(that)-350(t)27(w)28(o)-349(data)-350(sets)]TJ/F5 9.96 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TD[(\274)]TJ/F3 9.96 Tf 6.03 0 TD[(.)-444(W)82(e)-332(often)-333(use)-334(that)-333(v)55(alue)-333(of)]TJ/F5 9.96 Tf 125.39 0 TD[(\301)]TJ/F7 6.97 Tf 5.93 -1.49 TD[(uv)]TJ/F3 9.96 Tf 12.76 1.49 TD[(that)-333(liv)27(es)-332(in)-334(\()]TJ/F10 9.96 Tf 59.26 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(\274)-35(;)-167(\274)]TJ/F3 9.96 Tf 16.49 0 TD[(].)]TJ/F4 9.96 Tf -249.94 -20.91 TD[(Example)-383(4.2)]TJ/F3 9.96 Tf 0 -11.95 TD[(Let)]TJ/F5 9.96 Tf 17.78 0 TD[(u)]TJ/F3 9.96 Tf 5.71 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-277(=)-278(\()]TJ/F5 9.96 Tf 21.02 0 TD[(t;)-166(t)]TJ/F3 9.96 Tf 11.62 0 TD[(\))-326(and)]TJ/F5 9.96 Tf 26.43 0 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-277(=)-278(\()]TJ/F10 9.96 Tf 21.02 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(t;)-166(t)]TJ/F12 6.97 Tf 11.62 3.61 TD[(2)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\).)-442(Then)]TJ/F5 9.96 Tf 36.99 0 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.5 TD[(uv)]TJ/F3 9.96 Tf 9.44 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-277(=)]TJ/F5 9.96 Tf 17.15 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(2)]TJ/F3 9.96 Tf 6.55 -3.61 TD[(+)]TJ/F5 9.96 Tf 9.83 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(3)]TJ/F3 9.96 Tf 6.55 -3.61 TD[(+)]TJ/F5 9.96 Tf 9.83 0 TD[(tx)]TJ/F10 9.96 Tf 11.38 0 TD[(\241)]TJ/F5 9.96 Tf 9.83 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(2)]TJ/F5 9.96 Tf 4.47 -3.61 TD[(x)]TJ/F10 9.96 Tf 7.78 0 TD[(\241)]TJ/F3 9.96 Tf 9.83 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(ty)]TJ/F3 9.96 Tf 8.84 0 TD[(.)-442(Putting)]TJ/F5 9.96 Tf -322.23 -11.95 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.5 TD[(uv)]TJ/F3 9.96 Tf 9.45 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-349(equal)-350(to)-350(zero)-350(yields)-350(an)-350(ordinary)-350(line)-351(for)-350(ev)27(ery)]TJ/F5 9.96 Tf 210.74 0 TD[(t)]TJ/F10 9.96 Tf 6.64 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)-305(0.)-495(As)]TJ/F5 9.96 Tf 38.35 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-305(=)]TJ/F5 9.96 Tf 17.71 0 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F10 9.96 Tf 6.2 0 TD[(\241)]TJ/F5 9.96 Tf 10.07 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-305(=)]TJ -348.07 -13.77 TD[(\()]TJ/F10 9.96 Tf 3.88 0 TD[(\241)]TJ/F3 9.96 Tf 7.74 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t;)]TJ/F10 9.96 Tf 8.03 0 TD[(\241)]TJ/F5 9.96 Tf 7.74 0 TD[(t)]TJ/F3 9.96 Tf 5.37 0 TD[(+)]TJ/F5 9.96 Tf 9.53 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(2)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\),)-315(w)26(e)-310(ha)27(v)28(e)-311(lim)]TJ/F7 6.97 Tf 60.81 -1.5 TD[(t)]TJ/F17 6.97 Tf 3.01 0 TD[(!)]TJ/F12 6.97 Tf 7.94 0 TD[(0)]TJ/F7 6.97 Tf 7.38 6.55 TD[(d)]TJ/F12 6.97 Tf 4.15 0 TD[(\()]TJ/F7 6.97 Tf 3.11 0 TD[(t)]TJ/F12 6.97 Tf 3.01 0 TD[(\))]TJ/F14 4.98 Tf 3.11 -1 TD[(y)]TJ ET 0.4 w 114.57 -151.43 m 132.39 -151.43 l S BT/F7 6.97 Tf 114.57 -157.36 TD[(d)]TJ/F12 6.97 Tf 4.15 0 TD[(\()]TJ/F7 6.97 Tf 3.11 0 TD[(t)]TJ/F12 6.97 Tf 3.01 0 TD[(\))]TJ/F14 4.98 Tf 3.11 -0.99 TD[(x)]TJ/F3 9.96 Tf 8.4 4.43 TD[(=)]TJ/F12 6.97 Tf 11.71 3.92 TD[(1)]TJ ET 0.4 w 148.06 -151.43 m 152.03 -151.43 l S BT 148.06 -157.36 TD[(2)]TJ/F3 9.96 Tf 5.17 3.44 TD[(.)-436(The)-311(direction)-312(of)]TJ/F5 9.96 Tf 79.8 0 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.5 TD[(uv)]TJ/F3 9.96 Tf 9.44 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-311(at)]TJ/F5 9.96 Tf 18.93 0 TD[(t)]TJ/F3 9.96 Tf 6.37 0 TD[(=)-277(0)-311(is)-312(giv)27(en)-310(b)27(y)]TJ -298.05 -14.59 TD[(arctan\()]TJ/F12 6.97 Tf 32.77 3.92 TD[(1)]TJ ET 0.4 w 12.93 -166.02 m 16.9 -166.02 l S BT 12.93 -171.94 TD[(2)]TJ/F3 9.96 Tf 5.16 3.43 TD[(\))]TJ/F10 9.96 Tf 6.09 0 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(\274)]TJ/F3 9.96 Tf 6.03 0 TD[(,)-333(ho)27(w)28(ev)27(er,)-332(as)-333(the)-334(ruling)-333(sign)-333(rs\()]TJ/F5 9.96 Tf 137.48 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.49 TD[(x)]TJ/F3 9.96 Tf 5.02 1.49 TD[(\))-333(equals)]TJ/F10 9.96 Tf 37.4 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(1.)]TJ/F4 9.96 Tf -264.18 -20.92 TD[(Remark)-383(4.3)]TJ/F3 9.96 Tf 0 -11.95 TD[(Note)-399(that)-400(this)-399(de\257nition)-399(of)]TJ/F5 9.96 Tf 123.97 0 TD[(\301)]TJ/F7 6.97 Tf 5.94 -1.49 TD[(uv)]TJ/F3 9.96 Tf 13.42 1.49 TD[(indeed)-399(matc)27(hes)-398(with)-400(the)-399(direction)-400(of)-399(the)-399(directed)]TJ -143.33 -11.95 TD[(line)-347(that)-347(passes)-348(\257rst)-347(through)]TJ/F5 9.96 Tf 129.35 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-347(and)-347(then)-347(through)]TJ/F5 9.96 Tf 87.46 0 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-347(for)-347(small)-348(p)-27(ositiv)26(e)]TJ/F5 9.96 Tf 85.91 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(.)-486(F)82(or)-346(a)]TJ -332.13 -11.95 TD[(de\257nition)-343(that)-343(w)27(ould)-343(matc)27(h)-342(with)-343(small)-343(negativ)26(e)]TJ/F5 9.96 Tf 213.78 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(,)-345(w)26(e)-342(should)-343(tak)27(e)-342(in)26(to)-342(accoun)27(t)-342(the)]TJ -217.37 -11.95 TD[(o)-28(dness)-333(or)-333(ev)27(enness)-333(of)-333(the)-333(p)-28(o)27(w)27(er)-332(of)-333(the)-334(lo)27(w)28(est)-332(degree)-334(term)-333(of)]TJ/F5 9.96 Tf 266.82 0 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.5 TD[(uv)]TJ/F3 9.96 Tf 9.44 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\).)]TJ/F4 9.96 Tf -286.7 -20.92 TD[(Example)-383(4.4)]TJ/F3 9.96 Tf 0 -11.95 TD[(Let)]TJ/F5 9.96 Tf 18.56 0 TD[(u)]TJ/F3 9.96 Tf 9.74 0 TD[(and)]TJ/F5 9.96 Tf 20.08 0 TD[(v)]TJ/F3 9.96 Tf 9.22 0 TD[(b)-27(e)-405(as)-405(in)-405(Example)-405(4.2.)-659(F)82(or)-404(small)-405(negativ)27(e)]TJ/F5 9.96 Tf 189.04 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(,)-423(the)-405(direction)-405(of)-405(the)-405(line)]TJ/F5 9.96 Tf -250.23 -11.95 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.5 TD[(uv)]TJ/F3 9.96 Tf 12.82 1.5 TD[(that)-338(passes)-339(\257rst)-339(through)]TJ/F5 9.96 Tf 110.05 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-338(and)-339(then)-339(through)]TJ/F5 9.96 Tf 87.12 0 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-338(is)-339(close)-339(to)-338(arctan\()]TJ/F12 6.97 Tf 86.21 3.92 TD[(1)]TJ ET 0.4 w 305.15 -279.56 m 309.12 -279.56 l S BT 305.15 -285.49 TD[(2)]TJ/F3 9.96 Tf 5.16 3.44 TD[(\).)-460(If)-339(w)27(e)]TJ -330.15 -11.95 TD[(m)27(ultiply)-286(b)-28(oth)]TJ/F5 9.96 Tf 62.44 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-286(and)]TJ/F5 9.96 Tf 25.63 0 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-286(b)27(y)]TJ/F5 9.96 Tf 20.1 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(,)-295(that)-287(is)-287(c)26(hange)]TJ/F5 9.96 Tf 68.85 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-286(in)26(to)]TJ/F5 9.96 Tf 26.46 0 TD[(u)]TJ/F3 9.96 Tf 5.71 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-277(=)-278(\()]TJ/F5 9.96 Tf 21.02 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(2)]TJ/F5 9.96 Tf 4.47 -3.61 TD[(;)-166(t)]TJ/F12 6.97 Tf 8.02 3.61 TD[(2)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\))-286(and)]TJ/F5 9.96 Tf 25.63 0 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-286(in)26(to)]TJ/F5 9.96 Tf -339.13 -11.96 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-283(=)-285(\()]TJ/F10 9.96 Tf 21.15 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.62 TD[(2)]TJ/F5 9.96 Tf 4.46 -3.62 TD[(;)-166(t)]TJ/F12 6.97 Tf 8.03 3.62 TD[(3)]TJ/F3 9.96 Tf 4.46 -3.62 TD[(\),)-338(then)-337(the)-337(direction)-338(of)]TJ/F5 9.96 Tf 102.88 0 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.49 TD[(uv)]TJ/F3 9.96 Tf 12.8 1.49 TD[(for)-336(small)-338(negativ)27(e)]TJ/F5 9.96 Tf 80.7 0 TD[(t)]TJ/F3 9.96 Tf 6.96 0 TD[(and)-337(for)-337(small)-337(p)-28(ositiv)27(e)]TJ/F5 9.96 Tf -268.42 -11.95 TD[(t)]TJ/F3 9.96 Tf 6.92 0 TD[(b)-27(oth)-334(are)-333(close)-333(to)-334(arctan\()]TJ/F12 6.97 Tf 108.93 3.92 TD[(1)]TJ ET 0.4 w 96.01 -315.42 m 99.98 -315.42 l S BT 96.01 -321.34 TD[(2)]TJ/F3 9.96 Tf 5.16 3.43 TD[(\))]TJ/F10 9.96 Tf 6.09 0 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(\274)]TJ/F3 9.96 Tf 6.03 0 TD[(.)]TJ/F1 11.95 Tf -143.09 -30.87 TD[(4.2.2)-1125(Collinearit)30(y)94(.)]TJ/F3 9.96 Tf 0 -21.82 TD[(Let)]TJ/F5 9.96 Tf 17.23 0 TD[(u)]TJ/F3 9.96 Tf 5.71 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-166(v)]TJ/F3 9.96 Tf 9.61 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-271(and)]TJ/F5 9.96 Tf 25.33 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-271(b)-28(e)-272(three)-272(p)-27(olynomial)-272(sites.)-424(As)-272(long)-271(as)-272(the)-272(sites)-272(do)-271(not)-272(coincide)]TJ -91.56 -11.95 TD[(w)27(e)-319(can)-320(analyze)-320(whether)-320(they)-320(are)-321(collinear.)-440(Consider)-320(the)-320(determinan)27(t)]TJ/F5 9.96 Tf 303.3 0 TD[(D)]TJ/F3 9.96 Tf 8.52 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-319(giv)26(en)-319(b)27(y)]TJ/F5 9.96 Tf -247.51 -31.32 TD[(D)]TJ/F3 9.96 Tf 8.52 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-1277(=)]TJ/F5 9.96 Tf 37.07 0 TD[(D)]TJ/F7 6.97 Tf 8.25 -1.5 TD[(u;v)-35(;w)]TJ/F3 9.96 Tf 20.12 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-1277(=)]TJ/F15 9.96 Tf 37.07 20.42 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ/F3 9.96 Tf 8.3 21.51 TD[(1)]TJ/F5 9.96 Tf 15.79 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F7 6.97 Tf 3.88 -1.5 TD[(x)]TJ/F5 9.96 Tf 16.67 1.5 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.5 TD[(y)]TJ/F3 9.96 Tf -66.55 -10.45 TD[(1)]TJ/F5 9.96 Tf 16.05 0 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F7 6.97 Tf 3.88 -1.5 TD[(x)]TJ/F5 9.96 Tf 17.18 1.5 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.5 TD[(y)]TJ/F3 9.96 Tf -66.29 -10.46 TD[(1)]TJ/F5 9.96 Tf 14.94 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.49 TD[(x)]TJ/F5 9.96 Tf 14.98 1.49 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.49 TD[(y)]TJ/F15 9.96 Tf 9.77 33.77 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ/F5 9.96 Tf 4.98 9.46 TD[(:)]TJ/F3 9.96 Tf -288.2 -31.33 TD[(W)83(e)-495(call)-495(the)-496(three)-495(sites)]TJ/F4 9.96 Tf 108.37 0 TD[(collinear)]TJ/F3 9.96 Tf 47.19 0 TD[(if)]TJ/F5 9.96 Tf 10.75 0 TD[(D)]TJ/F3 9.96 Tf 8.52 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-495(is)-495(the)-496(n)27(ull)-494(p)-28(olynomial.)-931(Otherwise)-496(let)]TJ -182.3 -11.95 TD[(rs\()]TJ/F5 9.96 Tf 11.71 0 TD[(D)]TJ/F3 9.96 Tf 8.52 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-352(denote)-354(the)-353(ruling)-353(sign)-353(of)]TJ/F5 9.96 Tf 122.16 0 TD[(D)]TJ/F3 9.96 Tf 8.53 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\).)-503(If)-353(rs\()]TJ/F5 9.96 Tf 33.51 0 TD[(D)]TJ/F3 9.96 Tf 8.53 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-310(=)-311(1,)-358(w)27(e)-352(sa)27(y)-352(that)]TJ/F5 9.96 Tf 87.03 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-353(is)-353(on)-353(the)]TJ/F4 9.96 Tf -317.27 -11.95 TD[(left)]TJ/F3 9.96 Tf 19.63 0 TD[(of)-325(the)-325(p)-28(olynomial)-325(line)]TJ/F5 9.96 Tf 98.45 0 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.49 TD[(uv)]TJ/F3 9.96 Tf 9.44 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-325(at)]TJ/F5 9.96 Tf 19.2 0 TD[(t)]TJ/F3 9.96 Tf 6.37 0 TD[(=)-277(0,)-327(and)-325(if)-325(rs\()]TJ/F5 9.96 Tf 61.55 0 TD[(D)]TJ/F3 9.96 Tf 8.52 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\)\))-278(=)]TJ/F10 9.96 Tf 21.03 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(1,)-326(w)27(e)-325(sa)27(y)-324(that)]TJ/F5 9.96 Tf 64.21 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-325(is)]TJ -348.93 -11.95 TD[(on)-333(the)]TJ/F4 9.96 Tf 30.99 0 TD[(righ)32(t)]TJ/F3 9.96 Tf 24.12 0 TD[(.)]TJ/F4 9.96 Tf -55.11 -20.92 TD[(Example)-383(4.5)]TJ/F5 9.96 Tf 0 -11.95 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-363(=)-362(\(0)]TJ/F5 9.96 Tf 27.7 0 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stream
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TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\),)-410(and)]TJ/F5 9.96 Tf 30.7 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-394(are)-394(not)-395(collinear)-394(and)-395(that)-394(the)-395(circle)]TJ/F5 9.96 Tf 170.4 0 TD[(C)]TJ/F3 9.96 Tf 7.83 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)-166(v)]TJ/F3 9.96 Tf 9.61 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-166(w)]TJ/F3 9.96 Tf 11.83 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-394(is)]TJ -344.37 -11.95 TD[(orien)27(ted)-353(clo)-28(c)27(kwise.)-506(As)-354(long)-354(as)-354(the)-354(sites)-354(do)-355(not)-354(coincide,)-359(w)27(e)-353(can)-354(analyze)-355(if)-354(a)-354(fourth)]TJ 0 -11.95 TD[(p)-28(olynomial)-328(site)]TJ/F5 9.96 Tf 69.69 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-329(is)-328(inside)-329(or)-329(outside)-329(of)-329(the)-329(circle)-329(de\257ned)-328(b)26(y)]TJ/F5 9.96 Tf 194.27 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\),)]TJ/F5 9.96 Tf 9.93 0 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\),)-330(and)]TJ/F5 9.96 Tf 29.25 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\).)]TJ -356.1 -11.96 TD[(Consider)-333(the)-333(p)-28(olynomial)]TJ/F5 9.96 Tf 110.2 0 TD[(I)]TJ/F3 9.96 Tf 5.16 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F10 9.96 Tf 6.64 0 TD[(2)]TJ/F13 9.96 Tf 9.4 0 TD[(R)]TJ/F3 9.96 Tf 7.2 0 TD[([)]TJ/F5 9.96 Tf 2.76 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(])-333(de\257ned)-333(b)27(y)]TJ/F5 9.96 Tf -75.29 -47.76 TD[(I)]TJ/F3 9.96 Tf 5.16 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-1000(=)]TJ/F15 9.96 Tf 33.2 29.38 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ/F5 9.96 Tf 9.15 40.82 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.49 TD[(x)]TJ/F5 9.96 Tf 16.67 1.49 TD[(u)]TJ/F3 9.96 Tf 5.71 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.49 TD[(y)]TJ/F5 9.96 Tf 17.29 1.49 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F12 6.97 Tf 3.88 3.61 TD[(2)]TJ/F7 6.97 Tf 0 -6.07 TD[(x)]TJ/F3 9.96 Tf 7.22 2.46 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(u)]TJ/F3 9.96 Tf 5.71 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F12 6.97 Tf 3.87 3.61 TD[(2)]TJ/F7 6.97 Tf 0 -6.07 TD[(y)]TJ/F3 9.96 Tf 16.44 2.46 TD[(1)]TJ/F5 9.96 Tf -135.51 -14.79 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.49 TD[(x)]TJ/F5 9.96 Tf 17.19 1.49 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.49 TD[(y)]TJ/F5 9.96 Tf 18.07 1.49 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F12 6.97 Tf 3.88 3.62 TD[(2)]TJ/F7 6.97 Tf 0 -6.08 TD[(x)]TJ/F3 9.96 Tf 7.22 2.46 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F12 6.97 Tf 3.87 3.62 TD[(2)]TJ/F7 6.97 Tf 0 -6.08 TD[(y)]TJ/F3 9.96 Tf 16.96 2.46 TD[(1)]TJ/F5 9.96 Tf -136.62 -14.78 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.5 TD[(x)]TJ/F5 9.96 Tf 14.98 1.5 TD[(w)]TJ/F3 9.96 Tf 7.39 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F7 6.97 Tf 3.88 -1.5 TD[(y)]TJ/F5 9.96 Tf 14.74 1.5 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F12 6.97 Tf 3.88 3.61 TD[(2)]TJ/F7 6.97 Tf 0 -6.07 TD[(x)]TJ/F3 9.96 Tf 7.22 2.46 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F12 6.97 Tf 3.88 3.61 TD[(2)]TJ/F7 6.97 Tf 0 -6.07 TD[(y)]TJ/F3 9.96 Tf 14.74 2.46 TD[(1)]TJ/F5 9.96 Tf -135.32 -14.79 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.49 TD[(x)]TJ/F5 9.96 Tf 17.57 1.49 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F7 6.97 Tf 3.87 -1.49 TD[(y)]TJ/F5 9.96 Tf 18.64 1.49 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F12 6.97 Tf 3.88 3.62 TD[(2)]TJ/F7 6.97 Tf 0 -6.08 TD[(x)]TJ/F3 9.96 Tf 7.22 2.46 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F12 6.97 Tf 3.87 3.62 TD[(2)]TJ/F7 6.97 Tf 0 -6.08 TD[(y)]TJ/F3 9.96 Tf 17.34 2.46 TD[(1)]TJ/F15 9.96 Tf 9.96 51.35 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ 0 -5.97 TD[(\257)]TJ 0 -5.98 TD[(\257)]TJ/F5 9.96 Tf 4.98 18.43 TD[(:)]TJ/F3 9.96 Tf -282.83 -66.85 TD[(W)83(e)-245(call)-245(the)-246(four)-245(sites)]TJ/F4 9.96 Tf 91.22 0 TD[(co)-31(circular)]TJ/F3 9.96 Tf 51.49 0 TD[(at)]TJ/F5 9.96 Tf 11.3 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-277(0)-246(if)]TJ/F5 9.96 Tf 26.19 0 TD[(I)]TJ/F3 9.96 Tf 5.16 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-245(is)-246(the)-245(n)27(ull)-245(p)-28(olynomial.)-415(Let)-245(otherwise)]TJ -199.19 -11.95 TD[(rs\()]TJ/F5 9.96 Tf 11.71 0 TD[(I)]TJ/F3 9.96 Tf 5.16 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-376(denote)-377(the)-377(ruling)-378(sign)-377(of)]TJ/F5 9.96 Tf 123.6 0 TD[(I)]TJ/F3 9.96 Tf 5.16 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\).)-575(If)-377(rs\()]TJ/F5 9.96 Tf 34.47 0 TD[(I)]TJ/F3 9.96 Tf 5.16 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\)\))-351(=)-350(1,)-388(w)26(e)-376(sa)27(y)-376(that)]TJ/F5 9.96 Tf 88.86 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-377(is)]TJ/F4 9.96 Tf 18.08 0 TD[(outside)]TJ/F3 9.96 Tf -326.88 -11.96 TD[(of)-365(the)-364(p)-28(olynomial)-365(circle)]TJ/F5 9.96 Tf 107.24 0 TD[(c)]TJ/F7 6.97 Tf 4.31 -1.49 TD[(uv)-36(w)]TJ/F3 9.96 Tf 15.39 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-365(at)]TJ/F5 9.96 Tf 20 0 TD[(t)]TJ/F3 9.96 Tf 6.88 0 TD[(=)-330(0,)-372(and)-365(if)-365(rs\()]TJ/F5 9.96 Tf 63.32 0 TD[(D)]TJ/F3 9.96 Tf 8.52 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-330(=)]TJ/F10 9.96 Tf 22.07 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(1,)-372(w)27(e)-364(sa)27(y)-364(that)]TJ/F5 9.96 Tf 65.84 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-364(is)]TJ/F4 9.96 Tf -348.54 -11.95 TD[(inside)]TJ/F3 9.96 Tf 32 0 TD[(the)-315(circle.)-438(A)-315(set)-315(of)-315(p)-28(olynomial)-315(sites)]TJ/F5 9.96 Tf 157.3 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-314(is)-316(in)]TJ/F4 9.96 Tf 28.28 0 TD[(general)-362(p)-32(osition)]TJ/F3 9.96 Tf 82.64 0 TD[(at)]TJ/F5 9.96 Tf 11.99 0 TD[(t)]TJ/F3 9.96 Tf 6.37 0 TD[(=)-277(0,)-319(i\256)]TJ -332.73 -11.95 TD[(no)-333(three)-333(sites)-334(are)-333(collinear)-333(at)]TJ/F5 9.96 Tf 130.23 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-277(0)-334(and)-333(no)-333(four)-334(sites)-333(are)-333(co)-28(circular)-334(at)]TJ/F5 9.96 Tf 169.54 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-278(0.)]TJ/F4 9.96 Tf -312.49 -20.91 TD[(Example)-383(4.10)]TJ/F3 9.96 Tf 0 -11.96 TD[(Let)]TJ/F5 9.96 Tf 18.01 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\),)]TJ/F5 9.96 Tf 10.17 0 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\),)-353(and)]TJ/F5 9.96 Tf 29.69 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-349(b)-28(e)-350(as)-349(in)-350(Example)-350(4.8.)-493(Let)]TJ/F5 9.96 Tf 125.19 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-305(=)-305(\(0)]TJ/F5 9.96 Tf 26.55 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\).)-493(W)82(e)-348(c)26(hec)28(k)-348(whether)]TJ/F5 9.96 Tf -267 -11.95 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-366(is)-366(inside)-366(or)-367(outside)-366(of)-366(the)-367(clo)-28(c)27(kwise)-365(orien)27(ted)-366(circle)]TJ/F5 9.96 Tf 231.84 0 TD[(C)]TJ/F3 9.96 Tf 7.83 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(u)]TJ/F3 9.96 Tf 5.71 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-166(w)]TJ/F3 9.96 Tf 11.82 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)-166(v)]TJ/F3 9.96 Tf 9.61 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-366(at)]TJ/F5 9.96 Tf 23.9 0 TD[(t)]TJ/F3 9.96 Tf 6.91 0 TD[(=)-332(0.)]TJ -343.93 -11.95 TD[(As)]TJ/F5 9.96 Tf 14.32 0 TD[(I)]TJ/F3 9.96 Tf 5.16 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-277(=)-278(4)]TJ/F5 9.96 Tf 22.13 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(4)]TJ/F3 9.96 Tf 5.87 -3.61 TD[(+)]TJ/F5 9.96 Tf 9.15 0 TD[(O)]TJ/F3 9.96 Tf 7.87 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(5)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\),)-300(w)27(e)-292(conclude)-293(that)]TJ/F5 9.96 Tf 85.61 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-292(is)-293(outside)-293(of)]TJ/F5 9.96 Tf 61.3 0 TD[(C)]TJ/F3 9.96 Tf 7.83 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-167(w)]TJ/F3 9.96 Tf 11.83 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 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TD[(C)-71(H)]TJ/F3 9.96 Tf 16.92 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F3 9.96 Tf 6.69 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-380(are)]TJ -337.89 -11.95 TD[(on)-341(the)-342(righ)27(t)-341(of)-341(the)-342(directed)-342(line)-342(de\257ned)-341(b)27(y)]TJ/F5 9.96 Tf 189.49 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.32 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-341(and)]TJ/F5 9.96 Tf 26.72 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.2 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-341(that)-342(passes)-342(\257rst)-341(through)]TJ/F5 9.96 Tf -248.69 -11.95 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.32 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\).)-443(This)-334(orien)27(tation)-332(and)-334(the)-333(connectedness)-333(are)-334(inherited)-333(when)]TJ/F5 9.96 Tf 269.99 0 TD[(t)]TJ/F3 9.96 Tf 6.92 0 TD[(v)55(anishes.)]TJ -285.95 -11.95 TD[(\(ii\))-833(This)-333(follo)27(ws)-332(from)-334(Prop)-28(ert)27(y)-332(4.16.)]TJ -2.77 -11.95 TD[(\(iii\))-833(If)]TJ/F5 9.96 Tf 33.98 0 TD[(abc)]TJ/F3 9.96 Tf 16.84 0 TD[(is)-300(the)-300(clo)-28(c)27(kwise)-300(orien)27(tation)-299(of)-301(the)-300(V)82(oronoi)-299(circle)-300(de\257ned)-301(b)27(y)]TJ/F5 9.96 Tf 257.8 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.5 TD[(a)]TJ/F3 9.96 Tf 4.81 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\),)]TJ/F5 9.96 Tf 9.7 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(b)]TJ/F3 9.96 Tf 4 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\),)]TJ -356.09 -11.96 TD[(and)]TJ/F5 9.96 Tf 19.36 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.49 TD[(c)]TJ/F3 9.96 Tf 4.05 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\),)-333(then)]TJ/F5 9.96 Tf 32.65 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(c)]TJ/F3 9.96 Tf 4.06 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\()]TJ/F5 9.96 Tf 7.74 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-333(is)-333(on)-334(the)-333(righ)27(t)-333(of)]TJ/F5 9.96 Tf 83.64 0 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.49 TD[(ab)]TJ/F3 9.96 Tf 8.32 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-333(at)]TJ/F5 9.96 Tf 19.37 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-277(0.)]TJ/F18 9.96 Tf 130.43 0 TD[(\245)]TJ/F4 9.96 Tf -354.99 -20.91 TD[(Example)-383(4.18)]TJ/F3 9.96 Tf 0 -11.95 TD[(Consider)-361(the)-362(ordered)-362(set)]TJ/F5 9.96 Tf 111.44 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-325(=)]TJ/F10 9.96 Tf 18.1 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)-166(v)]TJ/F3 9.96 Tf 9.61 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-166(w)]TJ/F3 9.96 Tf 11.83 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F10 9.96 Tf 3.87 0 TD[(g)]TJ/F3 9.96 Tf 8.58 0 TD[(of)-362(p)-27(olynomial)-362(sites)-362(in)27(tro)-27(duced)-362(in)]TJ -218.42 -11.95 TD[(Example)-324(4.6.)-441(As)]TJ/F5 9.96 Tf 75.79 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-324(is)-325(on)-324(the)-324(left)-325(of)]TJ/F5 9.96 Tf 76.44 0 TD[(l)]TJ/F7 6.97 Tf 2.97 -1.5 TD[(uv)]TJ/F3 9.96 Tf 9.44 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-324(at)]TJ/F5 9.96 Tf 19.19 0 TD[(t)]TJ/F3 9.96 Tf 6.37 0 TD[(=)-277(0,)-326(the)-325(com)27(binatorial)-323(con)27(v)27(ex)-323(h)27(ull)]TJ/F5 9.96 Tf -212.54 -11.96 TD[(cC)-71(H)]TJ/F3 9.96 Tf 21.23 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\)\))-333(of)]TJ/F5 9.96 Tf 22.41 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-333(at)]TJ/F5 9.96 Tf 19.37 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-278(0)-333(is)-333(giv)27(en)-333(b)27(y)-332(132.)]TJ/F4 9.96 Tf -101.54 -20.91 TD[(Example)-383(4.19)]TJ/F3 9.96 Tf 0 -11.95 TD[(Let)]TJ/F5 9.96 Tf 18.16 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-329(=)]TJ/F10 9.96 Tf 18.19 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(q)]TJ/F12 6.97 Tf 4.45 -1.5 TD[(1)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-166(q)]TJ/F12 6.97 Tf 8.87 -1.5 TD[(2)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)-166(q)]TJ/F12 6.97 Tf 8.87 -1.5 TD[(3)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-166(q)]TJ/F12 6.97 Tf 8.87 -1.5 TD[(4)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F10 9.96 Tf 3.87 0 TD[(g)]TJ/F3 9.96 Tf 8.62 0 TD[(as)-364(in)-365(Example)-364(4.13.)-539(Then)]TJ/F5 9.96 Tf 118.3 0 TD[(cC)-71(H)]TJ/F3 9.96 Tf 21.23 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-364(at)]TJ/F5 9.96 Tf 23.86 0 TD[(t)]TJ/F3 9.96 Tf 6.89 0 TD[(=)-329(0)]TJ -346.72 -11.96 TD[(equals)-333(132.)]TJ/F1 14.34 Tf 0 -35.59 TD[(4.4)-1124(The)-553(V)93(oronoi)-552(diagram)-552(of)-553(a)-552(set)-553(of)-552(p)-31(oin)30(ts)-552(and)]TJ 36.75 -17.93 TD[(angles)-375(b)-31(et)30(w)32(een)-374(the)-375(p)-32(oin)31(ts.)]TJ/F3 9.96 Tf -36.75 -25.25 TD[(In)-334(this)-335(section)-335(w)26(e)-334(de\257ne)-335(the)-335(V)83(oronoi)-334(diagram)-335(of)-335(a)-335(set)-335(of)-335(p)-28(oin)27(ts)-334(and)-335(angles)-335(b)-28(et)27(w)28(een)]TJ 0 -11.95 TD[(the)-346(p)-28(oin)27(ts.)-484(This)-346(enables)-347(us)-347(to)-346(in)26(tro)-26(duce)-347(a)-347(V)83(oronoi)-346(diagram)-347(for)-347(a)-346(set)-347(of)-347(p)-27(olynomial)]TJ 0 -11.95 TD[(sites.)-531(Moreo)27(v)28(er,)-369(w)27(e)-361(connect)-362(the)-363(notions)-362(of)-362(p)-28(olynomial)-362(lines)-362(and)-363(p)-27(olynomial)-363(circles)]TJ 0 -11.95 TD[(in)-333(the)-333(con)27(text)-333(of)-333(V)82(oronoi)-332(diagrams.)]TJ/F1 11.95 Tf 0 -30.54 TD[(4.4.1)-1124(De\257nition.)]TJ/F3 9.96 Tf 0 -21.82 TD[(Supp)-27(ose)]TJ/F5 9.96 Tf 39.44 0 TD[(S)]TJ/F3 9.96 Tf 10.08 0 TD[(=)]TJ/F10 9.96 Tf 11.14 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(1)]TJ/F5 9.96 Tf 4.47 1.49 TD[(;)-166(:)-166(:)-167(:)-167(;)-166(p)]TJ/F7 6.97 Tf 27.14 -1.49 TD[(n)]TJ/F10 9.96 Tf 5.42 1.49 TD[(g)]TJ/F3 9.96 Tf 8.68 0 TD[(is)-370(a)-372(set)-371(of)]TJ/F5 9.96 Tf 46.71 0 TD[(n)]TJ/F3 9.96 Tf 9.68 0 TD[(not-necessarily)-370(distinct)-371(p)-28(oin)27(ts)-371(in)-371(the)-371(plane.)]TJ -172.75 -11.95 TD[(T)83(o)-443(ev)27(ery)-443(pair)-444(of)-443(p)-28(oin)27(ts)-443(\()]TJ/F5 9.96 Tf 112.12 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.49 TD[(i)]TJ/F5 9.96 Tf 3.31 1.49 TD[(;)-166(p)]TJ/F7 6.97 Tf 9.44 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.2 1.49 TD[(\))-443(w)27(e)-443(add)-444(an)-443(angle)]TJ/F5 9.96 Tf 86.56 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.49 TD[(ij)]TJ/F3 9.96 Tf 11.43 1.49 TD[(suc)27(h)-443(that)-444(the)-443(follo)26(wing)-442(rule)]TJ -238.45 -11.95 TD[(holds:)-443(if)-331(t)27(w)28(o)-330(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 87.73 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 6.61 1.49 TD[(and)]TJ/F5 9.96 Tf 19.35 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 7.49 1.49 TD[(are)-331(distinct)-331(then)-331(there)-331(is)-331(a)-331(unique)-331(line)-331(though)]TJ/F5 9.96 Tf 203.86 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 6.62 1.49 TD[(and)]TJ/F5 9.96 Tf -346.69 -11.95 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 7.54 1.5 TD[(that)-334(mak)27(es)-335(some)-335(angle)]TJ/F5 9.96 Tf 102.55 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.5 TD[(ij)]TJ/F10 9.96 Tf 9.81 1.5 TD[(2)]TJ/F13 9.96 Tf 9.44 0 TD[(R)]TJ/F5 9.96 Tf 7.19 0 TD[(=)]TJ/F3 9.96 Tf 4.98 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(\274)]TJ/F13 9.96 Tf 6.04 0 TD[(Z)]TJ/F3 9.96 Tf 9.98 0 TD[(with)-335(the)]TJ/F5 9.96 Tf 39.88 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-axis,)-335(directed)-335(from)]TJ/F10 9.96 Tf 88.15 0 TD[(\2411)]TJ/F3 9.96 Tf 21.05 0 TD[(to)]TJ/F10 9.96 Tf 12.19 0 TD[(1)]TJ/F3 9.96 Tf 9.96 0 TD[(;)-335(if)]TJ/F5 9.96 Tf -350.81 -11.95 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F3 9.96 Tf 6.64 1.5 TD[(and)]TJ/F5 9.96 Tf 19.36 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 7.52 1.5 TD[(do)-333(coincide)-333(then)-333(w)26(e)-332(allo)27(w)-333(ev)27(ery)-332(v)54(alue)-332(in)]TJ/F13 9.96 Tf 178.75 0 TD[(R)]TJ/F5 9.96 Tf 7.2 0 TD[(=)]TJ/F3 9.96 Tf 4.98 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(\274)]TJ/F13 9.96 Tf 6.03 0 TD[(Z)]TJ/F3 9.96 Tf 9.96 0 TD[(for)]TJ/F5 9.96 Tf 15.24 0 TD[(\256)]TJ/F7 6.97 Tf 6.38 -1.5 TD[(ij)]TJ/F3 9.96 Tf 7.01 1.5 TD[(.)]TJ -284.07 -15.39 TD[(Let)]TJ/F5 9.96 Tf 18.05 0 TD[(\260)]TJ/F7 6.97 Tf 5.15 -1.49 TD[(n)]TJ/F3 9.96 Tf 8.95 1.49 TD[(b)-27(e)-354(a)-354(set)-354(of)]TJ/F5 9.96 Tf 49.57 0 TD[(n)]TJ/F3 9.96 Tf 9.5 0 TD[(p)-27(oin)26(ts)]TJ/F5 9.96 Tf 30.14 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-167(:)-166(:)-167(:)-167(;)-166(p)]TJ/F7 6.97 Tf 27.15 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\))-354(and)]TJ/F15 9.96 Tf 26.97 8.07 TD[(\241)]TJ/F7 6.97 Tf 4.57 -3.65 TD[(n)]TJ/F12 6.97 Tf 0.47 -7.85 TD[(2)]TJ/F15 9.96 Tf 4.45 11.5 TD[(\242)]TJ/F3 9.96 Tf 8.09 -8.07 TD[(angles)]TJ/F5 9.96 Tf 30.14 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(12)]TJ/F5 9.96 Tf 8.44 1.49 TD[(;)-166(:)-167(:)-166(:)-167(;)-167(\256)]TJ/F12 6.97 Tf 28.5 -1.79 TD[(\()]TJ/F7 6.97 Tf 3.12 0 TD[(n)]TJ/F17 6.97 Tf 4.92 0 TD[(\241)]TJ/F12 6.97 Tf 6.22 0 TD[(1\))]TJ/F7 6.97 Tf 7.09 0 TD[(n)]TJ/F3 9.96 Tf 8.94 1.79 TD[(that)]TJ -344.47 -11.95 TD[(ob)-27(ey)-448(ab)-28(o)27(v)28(es)-448(rule.)-788(Fix)-448(t)27(w)27(o)-447(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 155.5 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 7.98 1.49 TD[(=)]TJ/F5 9.96 Tf 12.42 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.32 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\))-448(and)]TJ/F5 9.96 Tf 28.85 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 8.87 1.49 TD[(=)]TJ/F5 9.96 Tf 12.41 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.2 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\).)-788(The)]TJ/F4 9.96 Tf 36.11 0 TD[(bisection)]TJ -318.6 -11.95 TD[(p)-31(oin)31(t)]TJ/F5 9.96 Tf 30.25 0 TD[(b)]TJ/F3 9.96 Tf 4.27 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.49 TD[(i)]TJ/F5 9.96 Tf 3.31 1.49 TD[(;)-166(p)]TJ/F7 6.97 Tf 9.44 -1.49 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1.5 TD[(=)]TJ/F5 9.96 Tf 10.95 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 7.77 1.5 TD[(then)]TJ/F5 9.96 Tf 22.95 0 TD[(b)]TJ/F3 9.96 Tf 4.27 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.5 TD[(i)]TJ/F5 9.96 Tf 3.31 1.5 TD[(;)-166(p)]TJ/F7 6.97 Tf 9.44 -1.5 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\))-358(coincides)-360(with)-359(the)-359(double)]TJ -243.79 -11.95 TD[(p)-27(oin)27(t)]TJ/F5 9.96 Tf 26.24 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F3 9.96 Tf 6.49 1.5 TD[(=)]TJ/F5 9.96 Tf 10.91 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 4.19 1.5 TD[(.)-516(The)]TJ/F4 9.96 Tf 28.63 0 TD[(p)-31(erp)-32(endicular)-411(bisector)]TJ/F5 9.96 Tf 116.36 0 TD[(B)]TJ/F3 9.96 Tf 8.05 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F5 9.96 Tf 3.31 1.5 TD[(;)-166(p)]TJ/F7 6.97 Tf 9.44 -1.5 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\))-356(is)-358(the)-357(line)-357(through)]TJ/F5 9.96 Tf 92.02 0 TD[(b)]TJ/F3 9.96 Tf 4.27 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 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stream
 0.00 g 0.00 G BT/F3 9.96 Tf -19.84 30.56 TD[(52)]TJ/F6 9.96 Tf 186.72 0 TD[(Chapter)-333(4.)-778(Limits)-333(of)-334(V)83(oronoi)-333(diagrams.)]TJ/F3 9.96 Tf -186.72 -27.96 TD[(the)-351(shap)-28(e)-351(of)-351(the)-351(V)82(oronoi)-350(diagram)-351(of)]TJ/F5 9.96 Tf 162.1 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(.)-498(W)82(e)-350(c)27(haracterize)-350(those)-351(sites)-352(that)-351(determine)]TJ -168.78 -11.95 TD[(this)-374(shap)-28(e)-373(and)-374(presen)26(t)-373(an)-373(e\261cien)26(t)-373(algorithm)-374(to)-373(compute)-374(the)-374(shap)-28(e)-374(of)-374(the)-374(V)82(oronoi)]TJ 0 -11.95 TD[(diagram.)]TJ/F1 11.95 Tf 0 -32.53 TD[(4.5.1)-1125(The)-375(direction)-375(h)30(ull)-374(and)-375(p)-31(ositiv)30(e)-374(area)-375(cells.)]TJ/F3 9.96 Tf 0 -22.06 TD[(A)]TJ/F4 9.96 Tf 11.32 0 TD[(zero)-444(cluster)]TJ/F3 9.96 Tf 62.64 0 TD[(at)]TJ/F5 9.96 Tf 12.7 0 TD[(t)]TJ/F3 9.96 Tf 7.25 0 TD[(=)-365(0)-387(is)-386(a)-387(set)]TJ/F5 9.96 Tf 55.67 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-386(of)-387(p)-28(olynomial)-386(sites)-387(in)-386(general)-387(p)-27(osition)-387(suc)27(h)]TJ -163.73 -11.95 TD[(that)]TJ/F5 9.96 Tf 22.16 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.31 1.49 TD[(\(0\))-374(=)-373(\(0)]TJ/F5 9.96 Tf 36.77 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\))-391(for)-390(ev)26(ery)-390(site)]TJ/F5 9.96 Tf 74.34 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.32 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-390(in)]TJ/F5 9.96 Tf 19.96 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\).)-616(W)82(e)-390(w)27(an)27(t)-389(to)-391(kno)26(w)-390(the)-390(shap)-28(e)-391(of)-391(the)]TJ -195.93 -11.95 TD[(V)83(oronoi)-387(diagram)-387(of)-387(a)-388(zero)-387(cluster.)-607(F)83(or)-387(this)-387(purp)-28(ose)-387(it)-387(is)-388(enough)-387(to)-387(determine)-388(the)]TJ 0 -11.95 TD[(b)-28(oundary)-333(of)-333(the)-334(V)83(oronoi)-333(cells)-333(of)-333(p)-28(ositiv)27(e)-333(area)-333(at)]TJ/F5 9.96 Tf 214.06 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-277(0.)]TJ -220.42 -15.39 TD[(Assume)-338(that)]TJ/F5 9.96 Tf 58.58 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-337(is)-338(a)-338(zero)-337(cluster)-338(at)]TJ/F5 9.96 Tf 91.17 0 TD[(t)]TJ/F3 9.96 Tf 6.44 0 TD[(=)-284(0.)-458(Fix)-338(some)-337(site)]TJ/F5 9.96 Tf 84.13 0 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-337(in)-338(the)-338(com)27(binatorial)]TJ -267.13 -11.95 TD[(con)27(v)28(ex)-321(h)27(ull)]TJ/F5 9.96 Tf 52.06 0 TD[(cC)-71(H)]TJ/F3 9.96 Tf 21.23 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-321(at)]TJ/F5 9.96 Tf 23.01 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-278(0.)-440(There)-322(is)-322(one)-322(incoming)-322(edge)-322(and)-322(one)-321(outgoing)-322(edge)]TJ -120.69 -11.95 TD[(in)]TJ/F5 9.96 Tf 12.02 0 TD[(cC)-71(H)]TJ/F3 9.96 Tf 21.22 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-372(at)]TJ/F5 9.96 Tf 24.02 0 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-372(at)]TJ/F5 9.96 Tf 20.15 0 TD[(t)]TJ/F3 9.96 Tf 7.02 0 TD[(=)-343(0.)-562(Supp)-28(ose)-373(the)-373(incoming)-373(edge)-372(comes)-373(from)]TJ/F5 9.96 Tf 201.31 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\),)-382(while)]TJ -329.6 -11.95 TD[(the)-373(outgoing)-374(edges)-373(go)-28(es)-373(to)]TJ/F5 9.96 Tf 120.8 0 TD[(w)]TJ/F3 9.96 Tf 7.4 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\).)-564(Site)]TJ/F5 9.96 Tf 32.58 0 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-373(is)-374(called)-373(a)]TJ/F4 9.96 Tf 55.33 0 TD[(corner)-429(site)]TJ/F3 9.96 Tf 57.26 0 TD[(of)]TJ/F5 9.96 Tf 11.74 0 TD[(S)]TJ/F3 9.96 Tf 6.69 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-373(at)]TJ/F5 9.96 Tf 20.16 0 TD[(t)]TJ/F3 9.96 Tf 7.03 0 TD[(=)-344(0)]TJ -346.58 -11.95 TD[(if)-382(the)-381(direction)-382(of)-382(the)-382(incoming)-381(edge)-382(is)-382(distinct)-382(from)-381(the)-382(direction)-382(of)-382(the)-381(outgoing)]TJ 0 -11.96 TD[(edge,)-383(that)-372(is,)-383(if)]TJ/F5 9.96 Tf 70.72 0 TD[(\301)]TJ/F7 6.97 Tf 5.94 -1.49 TD[(uv)]TJ/F10 9.96 Tf 12.86 1.49 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 11.17 0 TD[(\301)]TJ/F7 6.97 Tf 5.93 -1.49 TD[(v)-36(w)]TJ/F3 9.96 Tf 10.69 1.49 TD[(.)-562(The)-373(corner)-373(sites)-373(of)]TJ/F5 9.96 Tf 94.5 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-372(at)]TJ/F5 9.96 Tf 20.15 0 TD[(t)]TJ/F3 9.96 Tf 7.02 0 TD[(=)-343(0)-373(are)-373(b)27(y)-372(de\257nition)-373(the)]TJ -253.13 -11.95 TD[(v)27(ertices)-380(of)-380(the)]TJ/F4 9.96 Tf 65.96 0 TD[(direction)-437(h)31(ull)]TJ/F5 9.96 Tf 71.24 0 TD[(D)-28(H)]TJ/F3 9.96 Tf 17.62 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-380(at)]TJ/F5 9.96 Tf 24.18 0 TD[(t)]TJ/F3 9.96 Tf 7.15 0 TD[(=)-355(0.)-586(Tw)27(o)-380(v)27(ertices)]TJ/F5 9.96 Tf 84.27 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))-380(and)]TJ/F5 9.96 Tf 27.5 0 TD[(v)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-380(are)]TJ -341.77 -13.44 TD[(connected)-361(b)27(y)-361(a)-361(directed)-362(edge)]TJ/F17 6.97 Tf 130.91 6.28 TD[(\241)194(!)]TJ/F5 9.96 Tf 0.96 -6.28 TD[(uv)]TJ/F3 9.96 Tf 15.45 0 TD[(if)-361(there)-361(are)-362(no)-361(corner)-361(sites)-362(on)-361(the)-362(path)-361(from)]TJ/F5 9.96 Tf 198.37 0 TD[(u)]TJ/F3 9.96 Tf 5.7 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ -358.86 -11.95 TD[(to)]TJ/F5 9.96 Tf 12.18 0 TD[(v)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-333(in)]TJ/F5 9.96 Tf 18.81 0 TD[(cC)-71(H)]TJ/F3 9.96 Tf 21.23 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\).)]TJ/F4 9.96 Tf -82.9 -20.91 TD[(Example)-383(4.32)]TJ/F3 9.96 Tf 0 -11.96 TD[(Let)]TJ/F5 9.96 Tf 19.24 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-510(=)]TJ/F10 9.96 Tf 21.79 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(q)]TJ/F12 6.97 Tf 4.45 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-166(:)-167(:)-167(:)-166(;)-167(q)]TJ/F12 6.97 Tf 26.58 -1.49 TD[(4)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F10 9.96 Tf 3.87 0 TD[(g)]TJ/F3 9.96 Tf 9.69 0 TD[(b)-28(e)-473(as)-473(in)27(tro)-27(duced)-473(in)-473(Example)-473(4.13.)-864(F)83(rom)-472(Example)]TJ -132.5 -11.95 TD[(4.18)-495(w)26(e)-494(kno)27(w)-495(that)]TJ/F5 9.96 Tf 89.74 0 TD[(cC)-71(H)]TJ/F3 9.96 Tf 21.23 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-495(equals)-495(132.)-932(Compare)-495(T)82(able)-494(4.1.)-932(The)-495(directions)]TJ/F5 9.96 Tf -129 -11.95 TD[(\301)]TJ/F12 6.97 Tf 5.94 -1.49 TD[(13)]TJ/F3 9.96 Tf 11.9 1.49 TD[(=)-347(arctan)]TJ/F12 6.97 Tf 40.1 3.92 TD[(3)]TJ ET 0.4 w 38.1 -278.51 m 42.07 -278.51 l S BT 38.1 -284.43 TD[(2)]TJ/F3 9.96 Tf 5.17 3.43 TD[(,)]TJ/F5 9.96 Tf 6.61 0 TD[(\301)]TJ/F12 6.97 Tf 5.93 -1.49 TD[(32)]TJ/F3 9.96 Tf 11.9 1.49 TD[(=)]TJ/F5 9.96 Tf 11.21 0 TD[(\274)]TJ/F10 9.96 Tf 8.53 0 TD[(\241)]TJ/F3 9.96 Tf 10.24 0 TD[(arctan)]TJ/F12 6.97 Tf 28.89 3.92 TD[(5)]TJ ET 0.4 w 126.58 -278.51 m 130.55 -278.51 l S BT 126.58 -284.43 TD[(2)]TJ/F3 9.96 Tf 8.9 3.43 TD[(and)]TJ/F5 9.96 Tf 19.79 0 TD[(\301)]TJ/F12 6.97 Tf 5.93 -1.49 TD[(21)]TJ/F3 9.96 Tf 11.91 1.49 TD[(=)]TJ/F10 9.96 Tf 11.21 0 TD[(\241)]TJ/F3 9.96 Tf 7.74 0 TD[(arctan)]TJ/F12 6.97 Tf 28.89 3.92 TD[(1)]TJ ET 0.4 w 220.95 -278.51 m 224.92 -278.51 l S BT 220.95 -284.43 TD[(2)]TJ/F3 9.96 Tf 8.91 3.43 TD[(are)-375(all)-375(distinct.)-571(It)-375(follo)27(ws)]TJ -249.7 -11.95 TD[(that)]TJ/F5 9.96 Tf 21.58 0 TD[(D)-28(H)]TJ/F3 9.96 Tf 17.61 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-277(=)]TJ/F5 9.96 Tf 21.02 0 TD[(cC)-72(H)]TJ/F3 9.96 Tf 21.23 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-277(=)-278(132)-333(at)]TJ/F5 9.96 Tf 51.46 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-277(0.)]TJ/F4 9.96 Tf -175.32 -20.92 TD[(Example)-383(4.33)]TJ/F3 9.96 Tf 0 -11.95 TD[(Let)]TJ/F5 9.96 Tf 19.22 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-507(=)]TJ/F10 9.96 Tf 21.72 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(q)]TJ/F12 6.97 Tf 4.45 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.46 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)-166(q)]TJ/F12 6.97 Tf 8.87 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-166(q)]TJ/F12 6.97 Tf 8.87 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F10 9.96 Tf 3.88 0 TD[(g)]TJ/F3 9.96 Tf 9.67 0 TD[(with)]TJ/F5 9.96 Tf 24.05 0 TD[(q)]TJ/F12 6.97 Tf 4.45 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-506(=)-507(\()]TJ/F10 9.96 Tf 25.59 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(t;)]TJ/F3 9.96 Tf 8.02 0 TD[(0\),)]TJ/F5 9.96 Tf 16.65 0 TD[(q)]TJ/F12 6.97 Tf 4.45 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-506(=)-507(\(0)]TJ/F5 9.96 Tf 30.57 0 TD[(;)-166(t)]TJ/F12 6.97 Tf 8.03 3.61 TD[(2)]TJ/F3 9.96 Tf 4.46 -3.61 TD[(\),)-505(and)]TJ/F5 9.96 Tf 32.41 0 TD[(q)]TJ/F12 6.97 Tf 4.45 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-506(=)]TJ -346.07 -11.95 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t;)]TJ/F10 9.96 Tf 8.02 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(2)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\).)-444(Then)]TJ/F5 9.96 Tf 37.07 0 TD[(cC)-71(H)]TJ/F3 9.96 Tf 21.23 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-277(=)-278(123,)-333(while)]TJ/F5 9.96 Tf 68.06 0 TD[(D)-27(H)]TJ/F3 9.96 Tf 17.61 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\)\))-278(=)-277(13,)-334(as)]TJ/F5 9.96 Tf 49.3 0 TD[(\301)]TJ/F12 6.97 Tf 5.94 -1.5 TD[(12)]TJ/F3 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Tf 3.87 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F5 9.96 Tf 3.32 1.49 TD[(;)-166(p)]TJ/F7 6.97 Tf 9.44 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.19 1.49 TD[(\))]TJ/F9 9.96 Tf -358.86 -11.95 TD[(p)50(asses)-356(thr)50(ough)]TJ/F3 9.96 Tf 65.8 0 TD[(\(0)]TJ/F5 9.96 Tf 8.85 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\))]TJ/F9 9.96 Tf 12.42 0 TD[(at)]TJ/F5 9.96 Tf 11.96 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-277(0)]TJ/F9 9.96 Tf 15.49 0 TD[(.)]TJ/F4 9.96 Tf -125.31 -25.33 TD[(Pro)-32(of.)]TJ/F3 9.96 Tf 35.98 0 TD[(The)-388(bisector)]TJ/F5 9.96 Tf 58.73 0 TD[(B)]TJ/F3 9.96 Tf 8.06 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F5 9.96 Tf 3.32 1.49 TD[(;)-166(p)]TJ/F7 6.97 Tf 9.43 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.2 1.49 TD[(\))-388(passes)-389(through)-388(the)-389(bisection)-388(p)-28(oin)27(t)]TJ/F5 9.96 Tf 162.91 0 TD[(b)]TJ/F3 9.96 Tf 4.27 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F5 9.96 Tf 3.31 1.49 TD[(;)-167(p)]TJ/F7 6.97 Tf 9.44 -1.49 TD[(j)]TJ/F3 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TD[(that)-379(has)-378(b)-28(oth)]TJ/F5 9.96 Tf -285.36 -11.95 TD[(u)]TJ/F3 9.96 Tf 8.97 0 TD[(and)]TJ/F5 9.96 Tf 19.32 0 TD[(v)]TJ/F3 9.96 Tf 8.45 0 TD[(on)-327(its)-328(b)-28(oundary)82(.)-441(The)-328(direction)-328(of)]TJ/F5 9.96 Tf 148.67 0 TD[(e)]TJ/F3 9.96 Tf 4.64 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(u;)-166(v)]TJ/F3 9.96 Tf 15.31 0 TD[(\))-328(is)-328(p)-28(erp)-27(endicular)-328(to)]TJ/F5 9.96 Tf 92.31 0 TD[(\301)]TJ/F7 6.97 Tf 5.93 -1.49 TD[(uv)]TJ/F3 9.96 Tf 9.44 1.49 TD[(.)-443(Edge)]TJ/F5 9.96 Tf -316.91 -11.95 TD[(e)]TJ/F3 9.96 Tf 4.64 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(u;)-166(v)]TJ/F3 9.96 Tf 15.31 0 TD[(\))-333(is)-333(orien)27(ted)-333(so)-333(that)-333(it)-334(mak)27(es)-332(an)-334(angle)-333(of)]TJ/F7 6.97 Tf 181.77 3.92 TD[(\274)]TJ ET 0.4 w 202.69 -78.57 m 207.6 -78.57 l S BT/F12 6.97 Tf 203.16 -84.5 TD[(2)]TJ/F3 9.96 Tf 8.96 3.44 TD[(with)]TJ/F5 9.96 Tf 22.68 0 TD[(\301)]TJ/F7 6.97 Tf 5.94 -1.5 TD[(uv)]TJ/F3 9.96 Tf 9.44 1.5 TD[(;)]TJ/F20 7.97 Tf -264.65 -11.95 TD[(3:)]TJ/F3 9.96 Tf 11.56 0 TD[(Determine)-333(those)-334(circles)-333(in)]TJ/F5 9.96 Tf 116.23 0 TD[(T)]TJ/F3 9.96 Tf 10.52 0 TD[(that)-333(ha)26(v)28(e)-332(p)-28(ositiv)27(e)-332(radius;)]TJ/F20 7.97 Tf -138.31 -11.96 TD[(4:)]TJ/F4 9.96 Tf 11.56 0 TD[(for)]TJ/F5 9.96 Tf 17.27 0 TD[(a)]TJ/F3 9.96 Tf 8.58 0 TD[(and)]TJ/F5 9.96 Tf 19.37 0 TD[(b)]TJ/F3 9.96 Tf 7.59 0 TD[(t)27(w)28(o)-333(lab)-27(els)-334(o)-28(ccurring)-333(in)-333(some)-334(circle)-333(of)-333(p)-28(ositiv)27(e)-333(radius)]TJ/F4 9.96 Tf 231.63 0 TD[(do)]TJ/F20 7.97 Tf -296 -11.95 TD[(5:)]TJ/F3 9.96 Tf 21.52 0 TD[(\(W)82(e)-332(sho)27(w)-333(ho)27(w)-332(to)-333(`dra)26(w')-332(the)-333(edge)]TJ/F5 9.96 Tf 148.66 0 TD[(ab)]TJ/F3 9.96 Tf 9.54 0 TD[(\).)]TJ/F20 7.97 Tf -179.72 -11.95 TD[(6:)]TJ/F3 9.96 Tf 21.52 0 TD[(Chec)27(k)-333(if)-333(w)27(e)-332(ha)26(v)28(e)-332(not)-334(dra)27(wn)]TJ/F5 9.96 Tf 124.53 0 TD[(ab)]TJ/F3 9.96 Tf 12.86 0 TD[(b)-27(efore)-334(in)-333(step)-333(2)-334(as)-333(an)-333(un)26(b)-26(ounded)-334(edge.)]TJ/F20 7.97 Tf -158.91 -11.95 TD[(7:)]TJ/F4 9.96 Tf 21.52 0 TD[(if)]TJ/F3 9.96 Tf 11.2 0 TD[(the)-344(com)27(bination)-344(of)-344(the)-344(lab)-28(els)]TJ/F5 9.96 Tf 130.91 0 TD[(a)]TJ/F3 9.96 Tf 8.7 0 TD[(and)]TJ/F5 9.96 Tf 19.48 0 TD[(b)]TJ/F3 9.96 Tf 7.7 0 TD[(o)-27(ccurs)-345(t)27(wice)-343(in)-344(the)-345(list)-344(of)-345(the)-344(circles)]TJ -177.99 -11.95 TD[(of)-333(p)-28(ositiv)27(e)-333(radius)]TJ/F4 9.96 Tf 78.16 0 TD[(then)]TJ/F20 7.97 Tf -99.68 -11.95 TD[(8:)]TJ/F3 9.96 Tf 31.48 0 TD[(there)-363(are)-363(t)27(w)28(o)-362(circle)-363(cen)27(ters)-362(distinct)-363(from)-363(\(0)]TJ/F5 9.96 Tf 191 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\).)-532(W)82(e)-362(connect)-363(the)-363(t)27(w)28(o)-362(circle)]TJ -195.43 -11.96 TD[(cen)27(ters)-333(b)27(y)-332(an)-333(edge)]TJ/F5 9.96 Tf 83.92 0 TD[(ab)]TJ/F3 9.96 Tf 9.54 0 TD[(;)]TJ/F20 7.97 Tf -124.94 -11.95 TD[(9:)]TJ/F4 9.96 Tf 21.52 0 TD[(else)-333(if)]TJ/F3 9.96 Tf 32.61 0 TD[(the)-333(com)27(bination)-332(of)-334(the)-333(lab)-28(els)-333(o)-28(ccurs)-333(only)-334(once)]TJ/F4 9.96 Tf 205.7 0 TD[(then)]TJ/F20 7.97 Tf -264.06 -11.95 TD[(10:)]TJ/F3 9.96 Tf 35.71 0 TD[(w)27(e)-333(connect)-333(the)-333(corresp)-28(onding)-333(circle)-334(cen)27(ter)]TJ/F5 9.96 Tf 188.03 0 TD[(c)]TJ/F7 6.97 Tf 4.31 -1.49 TD[(ab)]TJ/F3 9.96 Tf 11.64 1.49 TD[(to)-332(the)-334(origin.)]TJ -240.83 -17.37 TD[(Determining)-396(the)-396(shap)-28(e)-396(of)-397(the)-396(V)82(oronoi)-395(diagram)-396(is)-397(relativ)27(ely)-395(easy)82(,)-411(compare)-396(Section)]TJ 0 -11.96 TD[(4.5.)-465(W)82(e)-339(ha)27(v)27(e)-339(seen)-340(in)-341(this)-340(section,)-342(ho)27(w)28(ev)27(er,)-341(that)-340(the)-340(com)26(binatorial)-339(structure)-340(on)-341(the)]TJ 0 -11.95 TD[(b)-28(oundary)-333(itself)-333(can)-334(get)-333(rather)-333(complicated.)]TJ/F1 14.34 Tf 0 -42.26 TD[(4.7)-1125(Example:)-500(20)-375(p)-31(olynomial)-375(sites.)]TJ/F3 9.96 Tf 0 -26.43 TD[(In)-328(this)-329(section)-328(w)27(e)-328(analyze)-328(a)-328(sligh)26(tly)-327(bigger)-328(example,)-330(illustrating)-328(the)-329(tec)27(hniques)-327(and)]TJ 0 -11.95 TD[(theory)-397(dev)26(elop)-26(ed)-398(in)-398(the)-398(former)-397(sections.)-638(W)83(e)-397(consider)-398(a)-397(set)]TJ/F5 9.96 Tf 266.71 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-397(of)-398(20)-397(p)-28(olynomial)]TJ -280.86 -11.95 TD[(sites.)-584(W)83(e)-379(determine)-380(the)-380(shap)-28(e)-380(of)-380(the)-379(V)82(oronoi)-379(diagram)]TJ/F5 9.96 Tf 244.39 0 TD[(V)]TJ/F3 9.96 Tf 8.02 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\)\))-380(at)]TJ/F5 9.96 Tf 24.17 0 TD[(t)]TJ/F3 9.96 Tf 7.14 0 TD[(=)-354(0.)-584(Next)-380(w)27(e)]TJ -301.74 -11.95 TD[(fo)-28(cus)-268(on)-268(the)-268(outside)-269(edges)-268(of)]TJ/F5 9.96 Tf 124.93 0 TD[(V)]TJ/F3 9.96 Tf 8.02 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F3 9.96 Tf 6.69 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\)\))-267(at)]TJ/F5 9.96 Tf 21.94 0 TD[(t)]TJ/F3 9.96 Tf 6.36 0 TD[(=)-277(0.)-423(W)82(e)-267(visualize)-268(the)-269(p)-27(olynomial)-269(sites)-268(and)]TJ -179.28 -11.95 TD[(compare)-397(the)-397(outcome)-397(of)-398(the)-397(computation)-397(to)-397(the)-398(visualization.)-636(First)-397(w)27(e)-396(in)26(tro)-26(duce)]TJ 0 -11.96 TD[(the)-403(p)-27(olynomial)-403(sites.)]TJ/F5 9.96 Tf 98.19 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-402(is)-403(a)-403(set)-402(of)-403(20)-403(distinct)-403(sites)-402(\()]TJ/F5 9.96 Tf 133.35 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-166(:)-167(:)-167(:)-166(;)-167(p)]TJ/F12 6.97 Tf 27.15 -1.49 TD[(20)]TJ/F3 9.96 Tf 8.43 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\)\))-403(suc)27(h)-402(that)]TJ/F5 9.96 Tf -309.56 -11.95 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.32 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-277(=)-278(\(0)]TJ/F5 9.96 Tf 26.01 0 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(0\))-333(for)]TJ/F5 9.96 Tf 27.42 0 TD[(i)]TJ/F3 9.96 Tf 6.2 0 TD[(=)-277(1)]TJ/F5 9.96 Tf 15.49 0 TD[(;)-166(:)-167(:)-167(:)-166(;)]TJ/F3 9.96 Tf 22.13 0 TD[(20:)]TJ/F5 9.96 Tf -106.47 -37.44 TD[(p)]TJ/F12 6.97 Tf 5.02 -1.49 TD[(1)]TJ/F3 9.96 Tf 18.39 1.49 TD[(\(0)]TJ/F5 9.96 Tf 8.86 0 TD[(;)-166(t)]TJ/F12 6.97 Tf 8.02 3.61 TD[(5)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-11040(p)]TJ/F12 6.97 Tf 117.74 -1.49 TD[(11)]TJ/F3 9.96 Tf 18.4 1.49 TD[(\()]TJ/F10 9.96 Tf 3.87 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(2)]TJ/F10 9.96 Tf 6.68 -3.61 TD[(\241)]TJ/F3 9.96 Tf 9.96 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(4)]TJ/F5 9.96 Tf 4.47 -3.61 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F3 9.96 Tf 7.74 0 TD[(3)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F3 9.96 Tf 5.81 0 TD[(+)-222(2)]TJ/F5 9.96 Tf 14.94 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(2)]TJ/F10 9.96 Tf 6.68 -3.61 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(3)]TJ/F3 9.96 Tf 6.68 -3.61 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(4)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)]TJ -324.97 -11.95 TD[(p)]TJ/F12 6.97 Tf 5.02 -1.5 TD[(2)]TJ/F3 9.96 Tf 18.39 1.5 TD[(\(0)]TJ/F5 9.96 Tf 8.86 0 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F3 9.96 Tf 5.81 0 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(4)]TJ/F3 9.96 Tf 6.68 -3.61 TD[(+)-222(2)]TJ/F5 9.96 Tf 14.94 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(5)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-6424(p)]TJ/F12 6.97 Tf 71.77 -1.5 TD[(12)]TJ/F3 9.96 Tf 18.4 1.5 TD[(\()]TJ/F10 9.96 Tf 3.87 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F10 9.96 Tf 5.81 0 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(4)]TJ/F5 9.96 Tf 4.47 -3.61 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(3)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(2)]TJ/F3 9.96 Tf 6.69 -3.61 TD[(+)-221(3)]TJ/F5 9.96 Tf 14.94 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(3)]TJ/F10 9.96 Tf 6.68 -3.61 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(5)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)]TJ -292 -11.95 TD[(p)]TJ/F12 6.97 Tf 5.02 -1.5 TD[(3)]TJ/F3 9.96 Tf 18.39 1.5 TD[(\(2)]TJ/F5 9.96 Tf 8.86 0 TD[(t;)]TJ/F3 9.96 Tf 8.02 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(3)]TJ/F3 9.96 Tf 6.68 -3.61 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(4)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)-8146(p)]TJ/F12 6.97 Tf 88.92 -1.5 TD[(13)]TJ/F3 9.96 Tf 18.4 1.5 TD[(\()]TJ/F10 9.96 Tf 3.87 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.61 TD[(2)]TJ/F10 9.96 Tf 6.68 -3.61 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(4)]TJ/F5 9.96 Tf 4.47 -3.61 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F3 9.96 Tf 7.74 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(2)]TJ/F3 9.96 Tf 6.68 -3.61 TD[(+)-222(3)]TJ/F5 9.96 Tf 14.94 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.61 TD[(3)]TJ/F3 9.96 Tf 4.47 -3.61 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)]TJ -283.98 -11.96 TD[(p)]TJ/F12 6.97 Tf 5.02 -1.49 TD[(4)]TJ/F3 9.96 Tf 18.39 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.62 TD[(2)]TJ/F5 9.96 Tf 4.47 -3.62 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F3 9.96 Tf 5.81 0 TD[(+)-222(2)]TJ/F5 9.96 Tf 14.94 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.62 TD[(2)]TJ/F10 9.96 Tf 6.69 -3.62 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.62 TD[(3)]TJ/F3 9.96 Tf 4.47 -3.62 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-6115(p)]TJ/F12 6.97 Tf 68.69 -1.49 TD[(14)]TJ/F3 9.96 Tf 18.4 1.49 TD[(\()]TJ/F10 9.96 Tf 3.87 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(t)]TJ/F3 9.96 Tf 5.81 0 TD[(+)-221(3)]TJ/F5 9.96 Tf 14.94 0 TD[(t)]TJ/F12 6.97 Tf 3.59 3.62 TD[(2)]TJ/F10 9.96 Tf 6.68 -3.62 TD[(\241)]TJ/F3 9.96 Tf 9.96 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.62 TD[(3)]TJ/F3 9.96 Tf 6.68 -3.62 TD[(+)-222(3)]TJ/F5 9.96 Tf 14.94 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.62 TD[(4)]TJ/F5 9.96 Tf 4.47 -3.62 TD[(;)-166(t)]TJ/F3 9.96 Tf 10.23 0 TD[(+)-222(3)]TJ/F5 9.96 Tf 14.94 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.62 TD[(2)]TJ/F10 9.96 Tf 6.68 -3.62 TD[(\241)]TJ/F3 9.96 Tf 9.96 0 TD[(3)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.62 TD[(5)]TJ/F3 9.96 Tf 4.47 -3.62 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)]TJ -337.97 -11.95 TD[(p)]TJ/F12 6.97 Tf 5.02 -1.49 TD[(5)]TJ/F3 9.96 Tf 18.39 1.49 TD[(\()]TJ/F10 9.96 Tf 3.88 0 TD[(\241)]TJ/F3 9.96 Tf 7.74 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F12 6.97 Tf 3.6 3.62 TD[(4)]TJ/F5 9.96 Tf 4.47 -3.62 TD[(;)]TJ/F10 9.96 Tf 4.42 0 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TD[(c)]TJ/F10 9.96 Tf 7.08 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 10.51 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(.)-432(Let)]TJ/F5 9.96 Tf 24.57 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.31 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))-297(b)-28(e)-298(the)]TJ/F5 9.96 Tf 36.84 0 TD[(i)]TJ/F3 9.96 Tf 3.43 0 TD[(-th)-297(p)-28(oin)27(t)-297(of)-298(the)-298(con\257guration)]TJ/F5 9.96 Tf 129.12 0 TD[(c)]TJ/F3 9.96 Tf 7.28 0 TD[(and)]TJ -346.69 -11.95 TD[(let)]TJ/F5 9.96 Tf 15.07 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.5 TD[(ij)]TJ/F3 9.96 Tf 7.01 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 7.76 0 TD[(2)]TJ/F13 9.96 Tf 10.54 0 TD[(R)]TJ/F5 9.96 Tf 7.19 0 TD[(=)]TJ/F3 9.96 Tf 4.98 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(\274)]TJ/F13 9.96 Tf 6.04 0 TD[(Z)]TJ/F3 9.96 Tf 10.63 0 TD[(b)-27(e)-402(the)-401(angle)-401(b)-28(et)27(w)28(een)]TJ/F5 9.96 Tf 97.88 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F3 9.96 Tf 3.32 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))-401(and)]TJ/F5 9.96 Tf 27.91 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\).)-648(Note)-401(that)-402(for)-401(standard)]TJ -248.45 -11.95 TD[(represen)27(tativ)28(es)]TJ/F5 9.96 Tf 68.24 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))-326(=)]TJ/F5 9.96 Tf 18.12 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\))-326(=)-326(\(0)]TJ/F5 9.96 Tf 26.97 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\).)-531(W)82(e)-361(sho)26(w)-361(that)-362(in)-363(an)27(y)-362(case)-362(there)-362(exists)-363(some)]TJ -153.96 -11.96 TD[(lab)-28(els)]TJ/F5 9.96 Tf 28 0 TD[(u)]TJ/F3 9.96 Tf 9.02 0 TD[(and)]TJ/F5 9.96 Tf 19.37 0 TD[(v)]TJ/F3 9.96 Tf 8.5 0 TD[(suc)27(h)-333(that)]TJ/F5 9.96 Tf 44.05 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.49 TD[(uv)]TJ/F3 9.96 Tf 9.44 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 6.64 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 10.51 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.49 TD[(uv)]TJ/F3 9.96 Tf 9.44 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\).)]TJ -174.96 -15.38 TD[(Let)]TJ/F5 9.96 Tf 18.01 0 TD[(i)]TJ/F10 9.96 Tf 6.46 0 TD[(2)-304(f)]TJ/F3 9.96 Tf 14.65 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(;)-166(:)-167(:)-166(:)-167(;)-167(n)]TJ/F10 9.96 Tf 28.11 0 TD[(g)]TJ/F3 9.96 Tf 8.46 0 TD[(b)-27(e)-349(minimal)-349(suc)26(h)-348(that)]TJ/F5 9.96 Tf 96.96 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.31 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 6.9 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 10.78 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.31 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\).)-492(If)]TJ/F5 9.96 Tf 21.66 0 TD[(i)]TJ/F3 9.96 Tf 6.46 0 TD[(=)-304(2,)-353(then)]TJ/F5 9.96 Tf 44.89 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 6.9 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 10.78 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\),)]TJ -356.1 -11.95 TD[(therefore)]TJ/F5 9.96 Tf 43.43 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(12)]TJ/F3 9.96 Tf 8.44 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 9.3 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 13.17 0 TD[(\256)]TJ/F12 6.97 Tf 6.38 -1.49 TD[(12)]TJ/F3 9.96 Tf 8.43 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\).)-925(Assume)-493(that)]TJ/F5 9.96 Tf 77.53 0 TD[(i)-544(>)]TJ/F3 9.96 Tf 22.03 0 TD[(2.)-925(In)-493(this)-494(case)]TJ/F5 9.96 Tf 74.7 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))-545(=)]TJ/F5 9.96 Tf 22.48 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.46 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\))-544(=)]TJ -345.69 -11.95 TD[(\(cos)]TJ/F5 9.96 Tf 18.87 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(12)]TJ/F5 9.96 Tf 8.44 1.5 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(sin)]TJ/F5 9.96 Tf 13.89 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(12)]TJ/F3 9.96 Tf 8.44 1.5 TD[(\))-397(for)-397(some)]TJ/F5 9.96 Tf 49.31 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(12)]TJ/F10 9.96 Tf 12.27 1.5 TD[(2)]TJ/F3 9.96 Tf 10.47 0 TD[(\()]TJ/F10 9.96 Tf 3.87 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(\274)-35(;)-167(\274)]TJ/F3 9.96 Tf 16.49 0 TD[(].)-637(Let)]TJ/F5 9.96 Tf 30.37 0 TD[(m)]TJ/F3 9.96 Tf 12.7 0 TD[(b)-27(e)-398(the)-397(line)-398(through)]TJ/F5 9.96 Tf 89.73 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 8.43 1.5 TD[(and)]TJ/F5 9.96 Tf 20.01 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F3 9.96 Tf 3.31 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\).)]TJ -356.1 -11.95 TD[(If)]TJ/F5 9.96 Tf 11.28 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F3 9.96 Tf 3.32 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\))]TJ/F10 9.96 Tf 8.83 0 TD[(62)]TJ/F5 9.96 Tf 11.61 0 TD[(m)]TJ/F3 9.96 Tf 8.74 0 TD[(,)-499(then)]TJ/F5 9.96 Tf 31.74 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(i)]TJ/F3 9.96 Tf 3.32 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 8.84 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 12.71 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(i)]TJ/F3 9.96 Tf 3.32 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\).)-841(Assume)-466(that)]TJ/F5 9.96 Tf 76.14 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.5 TD[(i)]TJ/F3 9.96 Tf 3.31 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\))]TJ/F10 9.96 Tf 8.84 0 TD[(2)]TJ/F5 9.96 Tf 11.6 0 TD[(m)]TJ/F3 9.96 Tf 8.75 0 TD[(.)-841(If)]TJ/F5 9.96 Tf 22.42 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F10 9.96 Tf 9.44 1.5 TD[(62)]TJ/F5 9.96 Tf 11.6 0 TD[(m)]TJ/F3 9.96 Tf 8.75 0 TD[(,)-498(then)]TJ/F5 9.96 Tf -335.64 -11.96 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(i)]TJ/F3 9.96 Tf 3.32 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 6.64 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 10.52 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(i)]TJ/F3 9.96 Tf 3.31 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\).)]TJ -61.71 -15.38 TD[(W)83(e)-351(are)-351(left)-352(with)-351(the)-352(case)-351(that)]TJ/F5 9.96 Tf 134.98 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(1)]TJ/F5 9.96 Tf 4.47 1.49 TD[(;)-166(p)]TJ/F12 6.97 Tf 9.44 -1.49 TD[(2)]TJ/F5 9.96 Tf 4.46 1.49 TD[(;)-167(p)]TJ/F7 6.97 Tf 9.44 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.32 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))-351(and)]TJ/F5 9.96 Tf 26.92 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.32 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\))-351(are)-351(all)-352(collinear)-351(on)-352(line)]TJ/F5 9.96 Tf 111.25 0 TD[(m)]TJ/F3 9.96 Tf 8.74 0 TD[(.)-499(As)]TJ/F5 9.96 Tf -343.6 -11.95 TD[(c;)-166(d)]TJ/F10 9.96 Tf 16.69 0 TD[(62)]TJ/F6 9.96 Tf 9.41 0 TD[(CLCONF)]TJ/F7 6.97 Tf 42.33 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(,)-331(there)-331(exists)]TJ/F5 9.96 Tf 59.01 0 TD[(j)]TJ/F3 9.96 Tf 7.97 0 TD[(suc)28(h)-331(that)]TJ/F5 9.96 Tf 44 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.2 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 6.64 0 TD[(62)]TJ/F5 9.96 Tf 9.41 0 TD[(m)]TJ/F3 9.96 Tf 8.74 0 TD[(.)-443(If)]TJ/F5 9.96 Tf 17.13 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.19 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\))-277(=)]TJ/F5 9.96 Tf 17.15 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.2 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))-331(then)]TJ/F5 9.96 Tf 29.84 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.49 TD[(j)-58(i)]TJ/F3 9.96 Tf 7.02 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 6.64 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf -354.99 -11.95 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.5 TD[(j)-58(i)]TJ/F3 9.96 Tf 7.02 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\).)-579(Let)]TJ/F5 9.96 Tf 30.71 0 TD[(l)]TJ/F3 9.96 Tf 6.94 0 TD[(b)-27(e)-379(the)-378(line)-379(through)]TJ/F5 9.96 Tf 88.97 0 TD[(p)]TJ/F12 6.97 Tf 5.02 -1.5 TD[(1)]TJ/F3 9.96 Tf 8.23 1.5 TD[(and)]TJ/F5 9.96 Tf 19.82 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\).)-580(If)]TJ/F5 9.96 Tf 22.83 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\))]TJ/F10 9.96 Tf 7.4 0 TD[(2)]TJ/F5 9.96 Tf 10.15 0 TD[(l)]TJ/F3 9.96 Tf 3.17 0 TD[(,)-389(then)]TJ/F5 9.96 Tf 29.79 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(j)]TJ/F3 9.96 Tf 4.19 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 7.39 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 11.26 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\).)]TJ -356.1 -11.95 TD[(Finally)83(,)-333(if)]TJ/F5 9.96 Tf 44.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\))]TJ/F10 9.96 Tf 6.64 0 TD[(62)]TJ/F5 9.96 Tf 9.4 0 TD[(l)]TJ/F3 9.96 Tf 3.17 0 TD[(,)-333(then)]TJ/F5 9.96 Tf 28.77 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(\))]TJ/F10 9.96 Tf 6.64 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 10.52 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\).)]TJ/F18 9.96 Tf 180.31 0 TD[(\245)]TJ/F4 9.96 Tf -354.99 -20.92 TD[(Remark)-383(5.14)]TJ/F3 9.96 Tf 0 -11.95 TD[(Supp)-28(ose)-359(w)27(e)-359(are)-359(giv)27(en)-359(an)-359(image)-360(p)-27(oin)26(t)]TJ/F5 9.96 Tf 166.8 0 TD[(a)]TJ/F3 9.96 Tf 8.46 0 TD[(=)]TJ/F5 9.96 Tf 10.95 0 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.5 TD[(D)31(A)]TJ/F14 4.98 Tf 11.66 -0.99 TD[(n)]TJ/F3 9.96 Tf 5.38 2.49 TD[(\([)]TJ/F5 9.96 Tf 6.64 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(]\))-359(for)-360(some)-359([)]TJ/F5 9.96 Tf 53.71 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(])]TJ/F10 9.96 Tf 5.96 0 TD[(2)]TJ/F4 9.96 Tf 9.84 0 TD[(conf)]TJ/F7 6.97 Tf 20.69 -1.5 TD[(n)]TJ/F10 9.96 Tf 5.42 1.5 TD[(n)]TJ/F4 9.96 Tf 4.98 0 TD[(clconf)]TJ/F7 6.97 Tf 28.95 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(.)]TJ -359.97 -11.95 TD[(W)83(e)-499(construct)-500(the)-500(standard)-499(represen)26(tativ)28(e)-499(from)-499(the)-500(angles)-500(in)]TJ/F5 9.96 Tf 280.88 0 TD[(a)]TJ/F3 9.96 Tf 10.24 0 TD[(as)-499(follo)27(ws.)-943(Put)]TJ/F5 9.96 Tf -291.12 -11.95 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 7.63 1.5 TD[(=)-316(\(0)]TJ/F5 9.96 Tf 19.75 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\))-356(and)]TJ/F5 9.96 Tf 32 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 7.63 1.5 TD[(=)-316(\(cos)]TJ/F5 9.96 Tf 29.76 0 TD[(\256)]TJ/F12 6.97 Tf 6.38 -1.5 TD[(12)]TJ/F5 9.96 Tf 8.43 1.5 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(sin)]TJ/F5 9.96 Tf 13.89 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(12)]TJ/F3 9.96 Tf 8.44 1.5 TD[(\).)-514(A)-357(p)-27(oin)26(t)]TJ/F5 9.96 Tf 49.02 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.5 TD[(i)]TJ/F3 9.96 Tf 6.86 1.5 TD[(is)-357(on)-356(the)-357(line)]TJ/F5 9.96 Tf 60.75 0 TD[(l)]TJ/F12 6.97 Tf 2.97 -1.5 TD[(12)]TJ/F3 9.96 Tf 11.99 1.5 TD[(through)]TJ/F5 9.96 Tf 37.89 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 8.02 1.5 TD[(and)]TJ/F5 9.96 Tf -346.69 -11.96 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 7.79 1.49 TD[(if)-333(and)-333(only)-334(if)]TJ ET 0.4 w 96.64 -486.69 m 111.45 -486.69 l S BT/F5 9.96 Tf 96.64 -492.37 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(12)]TJ/F3 9.96 Tf 11.21 1.5 TD[(=)]TJ ET 0.4 w 124.73 -486.69 m 138.39 -486.69 l S BT/F5 9.96 Tf 124.73 -492.37 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(i)]TJ/F3 9.96 Tf 6.09 1.5 TD[(=)]TJ ET 0.4 w 151.67 -486.69 m 165.33 -486.69 l S BT/F5 9.96 Tf 151.67 -492.37 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(i)]TJ/F3 9.96 Tf 13.28 1.5 TD[(mo)-27(d)]TJ/F5 9.96 Tf 22.41 0 TD[(\274)-35(:)]TJ/F3 9.96 Tf 124.72 0 TD[(\(5.1\))]TJ -342.26 -21.55 TD[(As)-305([)]TJ/F5 9.96 Tf 17.21 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(])]TJ/F10 9.96 Tf 5.53 0 TD[(2)]TJ/F4 9.96 Tf 9.41 0 TD[(conf)]TJ/F7 6.97 Tf 20.68 -1.49 TD[(n)]TJ/F10 9.96 Tf 5.42 1.49 TD[(n)]TJ/F4 9.96 Tf 4.98 0 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stream
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9.96 Tf 11.11 0 TD[(\241)]TJ/F12 6.97 Tf 8.94 3.92 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 81.8 -6.86 m 90.68 -6.86 l S BT/F12 6.97 Tf 84.26 -12.79 TD[(3)]TJ/F3 9.96 Tf 11.3 3.44 TD[(giv)28(es)]TJ/F5 9.96 Tf 24.76 0 TD[(r)]TJ/F17 6.97 Tf 4.77 3.61 TD[(0)]TJ/F3 9.96 Tf 6.16 -3.61 TD[(=)]TJ/F10 9.96 Tf 11.11 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(z)-43(;)-167(x;)-166(y)]TJ/F10 9.96 Tf 24.85 0 TD[(g)]TJ/F3 9.96 Tf 4.98 0 TD[(,)-378(while)]TJ/F5 9.96 Tf 32.9 0 TD[(\301)]TJ/F3 9.96 Tf 9.3 0 TD[(=)]TJ/F12 6.97 Tf 12.31 3.92 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 231.68 -6.86 m 240.56 -6.86 l S BT/F12 6.97 Tf 234.13 -12.79 TD[(3)]TJ/F3 9.96 Tf 11.3 3.44 TD[(leads)-369(to)]TJ/F5 9.96 Tf 37.84 0 TD[(r)]TJ/F17 6.97 Tf 4.78 3.61 TD[(0)]TJ/F3 9.96 Tf 6.15 -3.61 TD[(=)]TJ/F10 9.96 Tf 11.11 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(y)-36(;)-167(z)-44(;)-166(x)]TJ/F10 9.96 Tf 24.86 0 TD[(g)]TJ/F3 9.96 Tf 4.98 0 TD[(.)]TJ -359.97 -11.95 TD[(This)-333(explains)-333(the)-334(action)-333(corresp)-28(onding)-333(to)-334(the)-333(order)-333(three)-334(elemen)27(ts)-332(of)]TJ/F5 9.96 Tf 305.25 0 TD[(S)]TJ/F12 6.97 Tf 6.1 -1.5 TD[(3)]TJ/F3 9.96 Tf 4.47 1.5 TD[(.)]TJ/F18 9.96 Tf 39.17 0 TD[(\245)]TJ/F4 9.96 Tf -354.99 -20.92 TD[(Lemma)-383(5.37)]TJ/F9 9.96 Tf 0 -11.95 TD[(If)]TJ/F3 9.96 Tf 10.39 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x;)-167(y)-35(;)-167(z)]TJ/F3 9.96 Tf 24.86 0 TD[(\))]TJ/F10 9.96 Tf 6.64 0 TD[(2)]TJ/F5 9.96 Tf 9.41 0 TD[(\303)]TJ/F23 6.97 Tf 6.48 -1.49 TD[(D)28(A)]TJ/F16 4.98 Tf 11.98 -1 TD[(3)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F6 9.96 Tf 3.87 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\))]TJ/F9 9.96 Tf 3.87 0 TD[(,)-352(then)-351(also)]TJ/F3 9.96 Tf 48.93 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 7.76 0 TD[(+)]TJ/F5 9.96 Tf 9.81 0 TD[(\275;)-166(y)]TJ/F3 9.96 Tf 16.87 0 TD[(+)]TJ/F5 9.96 Tf 9.81 0 TD[(\275;)-166(z)]TJ/F3 9.96 Tf 16.71 0 TD[(+)]TJ/F5 9.96 Tf 9.81 0 TD[(\275)]TJ/F3 9.96 Tf 5.15 0 TD[(\))]TJ/F10 9.96 Tf 6.64 0 TD[(2)]TJ/F5 9.96 Tf 9.4 0 TD[(\303)]TJ/F23 6.97 Tf 6.49 -1.49 TD[(D)29(A)]TJ/F16 4.98 Tf 11.98 -1 TD[(3)]TJ/F3 9.96 Tf 4.38 2.49 TD[(\()]TJ/F6 9.96 Tf 3.88 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\))]TJ/F9 9.96 Tf 7.36 0 TD[(for)-351(any)]TJ/F5 9.96 Tf -331.37 -11.95 TD[(\275)]TJ/F10 9.96 Tf 7.92 0 TD[(2)]TJ/F3 9.96 Tf 9.41 0 TD[([0)]TJ/F5 9.96 Tf 7.74 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(\274)]TJ/F3 9.96 Tf 6.03 0 TD[(\))]TJ/F9 9.96 Tf 3.88 0 TD[(.)]TJ/F4 9.96 Tf -44.39 -33.14 TD[(Pro)-32(of.)]TJ/F3 9.96 Tf 35.98 0 TD[(A)-236(rotation)-236(of)]TJ/F5 9.96 Tf 57.43 0 TD[(\275)]TJ/F10 9.96 Tf 7.92 0 TD[(2)]TJ/F3 9.96 Tf 9.41 0 TD[([0)]TJ/F5 9.96 Tf 7.74 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(\274)]TJ/F3 9.96 Tf 6.03 0 TD[(\))-236(of)-236(the)-236(baseline,)-255(that)-236(is)-236(the)-236(axis)-236(with)-236(resp)-28(ect)-236(to)-236(whic)27(h)]TJ -133.92 -11.95 TD[(angles)-333(are)-333(measured,)-334(corresp)-28(onds)-333(to)-333(adding)]TJ/F5 9.96 Tf 193.17 0 TD[(\275)]TJ/F3 9.96 Tf 8.47 0 TD[(to)-333(all)-333(angles)]TJ/F5 9.96 Tf 55.94 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(12)]TJ/F3 9.96 Tf 8.44 1.5 TD[(,)]TJ/F5 9.96 Tf 6.09 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(13)]TJ/F3 9.96 Tf 11.76 1.5 TD[(and)]TJ/F5 9.96 Tf 19.36 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(23)]TJ/F3 9.96 Tf 8.44 1.5 TD[(.)]TJ/F18 9.96 Tf 24.21 0 TD[(\245)]TJ/F3 9.96 Tf -354.99 -33.15 TD[(Lemmata)-415(5.36)-414(and)-415(5.37)-415(suggest)-415(to)-414(consider)-415(the)-415(set)-415(of)-414(all)-415(p)-28(ossible)-415(angles)-414(b)-28(et)27(w)28(een)]TJ 0 -11.95 TD[(three)-418(distinct)-419(p)-27(oin)26(ts)-417(up)-419(to)-418(the)-418(p)-28(erm)27(utations)-418(and)-418(baseline)-419(rotations)-418(in)27(tro)-27(duced)-419(in)]TJ 0 -11.95 TD[(the)-387(lemmata.)-606(De\257ne)-387(\251)]TJ/F12 6.97 Tf 102.7 3.62 TD[(3)]TJ/F7 6.97 Tf 0 -6.08 TD[(p;r)]TJ/F3 9.96 Tf 14.54 2.46 TD[(:=)]TJ/F5 9.96 Tf 14.17 0 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.49 TD[(D)30(A)]TJ/F16 4.98 Tf 11.66 -1 TD[(3)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F6 9.96 Tf 3.87 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(=)]TJ/F10 9.96 Tf 8.65 0 TD[(\273)]TJ/F17 6.97 Tf 7.74 -1.8 TD[(f)]TJ/F7 6.97 Tf 4.08 0 TD[(p;r)]TJ/F17 6.97 Tf 10.39 0 TD[(g)]TJ/F3 9.96 Tf 4.58 1.8 TD[(,)-400(the)]TJ/F4 9.96 Tf 24.44 0 TD[(fundamen)31(tal)-444(image)]TJ/F3 9.96 Tf 99.76 0 TD[(of)]TJ/F5 9.96 Tf -354.71 -11.95 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.49 TD[(D)30(A)]TJ/F16 4.98 Tf 11.66 -1 TD[(3)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F6 9.96 Tf 3.87 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\),)-333(as)-333(the)-334(image)]TJ/F5 9.96 Tf 68.11 0 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.49 TD[(D)30(A)]TJ/F16 4.98 Tf 11.66 -1 TD[(3)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F6 9.96 Tf 3.87 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\))-333(up)-333(to)-334(p)-27(erm)26(utations)-332(and)-333(rotations.)]TJ/F4 9.96 Tf -187.69 -20.92 TD[(Corollary)-399(5.38)]TJ/F5 9.96 Tf 0 -11.95 TD[(\303)]TJ/F23 6.97 Tf 6.49 -1.49 TD[(D)29(A)]TJ/F16 4.98 Tf 11.98 -1 TD[(3)]TJ/F3 9.96 Tf 4.38 2.49 TD[(\()]TJ/F6 9.96 Tf 3.88 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\))]TJ/F9 9.96 Tf 7.75 0 TD[(up)-389(to)-389(b)50(aseline)-389(r)50(otations)-388(is)-390(obtaine)50(d)-388(by)-390(pr)50(oje)52(cting)]TJ/F5 9.96 Tf 216.33 0 TD[(\303)]TJ/F23 6.97 Tf 6.49 -1.49 TD[(D)29(A)]TJ/F16 4.98 Tf 11.98 -1 TD[(3)]TJ/F3 9.96 Tf 4.38 2.49 TD[(\()]TJ/F6 9.96 Tf 3.87 0 TD[(CONF)]TJ/F12 6.97 Tf 28.92 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.46 1.49 TD[(\))]TJ/F9 9.96 Tf 7.76 0 TD[(on)]TJ -352.05 -11.95 TD[(the)-358(plane)]TJ/F5 9.96 Tf 43.02 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(12)]TJ/F3 9.96 Tf 10.65 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(13)]TJ/F3 9.96 Tf 10.65 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.38 -1.49 TD[(23)]TJ/F3 9.96 Tf 11.2 1.49 TD[(=)-277(0)]TJ/F9 9.96 Tf 15.49 0 TD[(.)]TJ/F4 9.96 Tf -130.05 -33.14 TD[(Pro)-32(of.)]TJ/F3 9.96 Tf 35.98 0 TD[(This)-327(follo)27(ws)-326(directly)-327(from)-327(Lemma)-327(5.37,)-328(as)-327(an)27(y)-326(v)27(ector)-326(\()]TJ/F5 9.96 Tf 238.87 0 TD[(\275;)-166(\275;)-167(\275)]TJ/F3 9.96 Tf 24.3 0 TD[(\))-326(is)-327(orthogonal)]TJ -299.15 -11.95 TD[(to)-333(the)-333(plane)]TJ/F5 9.96 Tf 55.89 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(12)]TJ/F3 9.96 Tf 10.65 1.5 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(13)]TJ/F3 9.96 Tf 10.65 1.5 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.38 -1.5 TD[(23)]TJ/F3 9.96 Tf 11.2 1.5 TD[(=)-277(0.)]TJ/F18 9.96 Tf 227.56 0 TD[(\245)]TJ/F3 9.96 Tf -354.99 -33.14 TD[(W)83(e)-361(can)-361(actually)-362(construct)-361(the)-362(pro)-55(jection)]TJ/F5 9.96 Tf 183.28 0 TD[(\274)]TJ/F7 6.97 Tf 5.68 -1.5 TD[(r)]TJ/F3 9.96 Tf 8.01 1.5 TD[(on)-361(the)-361(plane)]TJ/F5 9.96 Tf 58.39 0 TD[(P)]TJ/F3 9.96 Tf 11.01 0 TD[(:)]TJ/F5 9.96 Tf 7.65 0 TD[(\256)]TJ/F12 6.97 Tf 6.38 -1.5 TD[(12)]TJ/F3 9.96 Tf 10.83 1.5 TD[(+)]TJ/F5 9.96 Tf 10.15 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(13)]TJ/F3 9.96 Tf 10.84 1.5 TD[(+)]TJ/F5 9.96 Tf 10.15 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(23)]TJ/F3 9.96 Tf 11.67 1.5 TD[(=)-324(0)]TJ -346.78 -11.96 TD[(as)-366(follo)26(ws.)]TJ/F5 9.96 Tf 50.13 0 TD[(u)]TJ/F12 6.97 Tf 5.71 -1.49 TD[(1)]TJ/F3 9.96 Tf 7.78 1.49 TD[(=)-333(\(1)]TJ/F5 9.96 Tf 19.92 0 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(1)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(0\))-366(and)]TJ/F5 9.96 Tf 32.21 0 TD[(u)]TJ/F12 6.97 Tf 5.7 -1.49 TD[(2)]TJ/F3 9.96 Tf 7.79 1.49 TD[(=)-332(\()]TJ/F12 6.97 Tf 16.13 3.93 TD[(1)]TJ ET 0.4 w 147.11 -312.73 m 151.08 -312.73 l S BT 147.11 -318.65 TD[(2)]TJ/F5 9.96 Tf 5.17 3.43 TD[(;)]TJ/F12 6.97 Tf 5.62 3.93 TD[(1)]TJ ET 0.4 w 157.9 -312.73 m 161.87 -312.73 l S BT 157.9 -318.65 TD[(2)]TJ/F5 9.96 Tf 5.16 3.43 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(1\))-366(form)-366(an)-367(orthogonal)-367(basis)-366(of)]TJ/F5 9.96 Tf 137.17 0 TD[(P)]TJ/F3 9.96 Tf 7.77 0 TD[(.)-544(Let)]TJ/F5 9.96 Tf -340.02 -11.95 TD[(e)]TJ/F12 6.97 Tf 4.64 -1.49 TD[(1)]TJ/F3 9.96 Tf 7.79 1.49 TD[(and)]TJ/F5 9.96 Tf 19.37 0 TD[(e)]TJ/F12 6.97 Tf 4.63 -1.49 TD[(2)]TJ/F3 9.96 Tf 7.79 1.49 TD[(b)-27(e)-334(the)-333(corresp)-28(onding)-333(unit)-333(length)-334(v)27(ectors.)-443(Then)]TJ/F5 9.96 Tf 209.91 0 TD[(\274)]TJ/F7 6.97 Tf 5.67 -1.49 TD[(r)]TJ/F3 9.96 Tf 7.73 1.49 TD[(is)-333(giv)27(en)-333(b)27(y)]TJ/F5 9.96 Tf -166.06 -24.05 TD[(\274)]TJ/F7 6.97 Tf 5.68 -1.5 TD[(r)]TJ/F3 9.96 Tf 7.17 1.5 TD[(:)]TJ/F13 9.96 Tf 12.73 0 TD[(R)]TJ/F12 6.97 Tf 7.19 3.61 TD[(3)]TJ/F10 9.96 Tf 14.43 -3.61 TD[(!)]TJ/F13 9.96 Tf 19.92 0 TD[(R)]TJ/F12 6.97 Tf 7.2 3.61 TD[(2)]TJ/F5 9.96 Tf 4.46 -3.61 TD[(;)]TJ -53.2 -11.95 TD[(c)]TJ/F10 9.96 Tf 21.62 0 TD[(7!)]TJ/F3 9.96 Tf 19.92 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(<)-277(c;)-166(e)]TJ/F12 6.97 Tf 23.88 -1.5 TD[(1)]TJ/F5 9.96 Tf 7.24 1.5 TD[(>;)-166(<)-278(c;)-166(e)]TJ/F12 6.97 Tf 36.06 -1.5 TD[(2)]TJ/F5 9.96 Tf 7.23 1.5 TD[(>)]TJ/F3 9.96 Tf 7.75 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(:)]TJ -258.5 -24.81 TD[(\274)]TJ/F7 6.97 Tf 5.68 -1.5 TD[(r)]TJ/F3 9.96 Tf 4.41 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\303)]TJ/F12 6.97 Tf 6.49 -1.5 TD[(D)30(A)]TJ/F16 4.98 Tf 11.66 -0.99 TD[(3)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F6 9.96 Tf 3.87 0 TD[(CONF)]TJ/F12 6.97 Tf 28.91 -1.5 TD[(3)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\)\))-333(is)-333(sho)26(wn)-332(on)-333(the)-334(left)-333(in)-333(Figure)-334(5.10.)]TJ/F4 9.96 Tf -73.75 -20.92 TD[(Remark)-383(5.39)]TJ/F5 9.96 Tf 0 -11.95 TD[(\274)]TJ/F7 6.97 Tf 5.68 -1.49 TD[(r)]TJ/F3 9.96 Tf 9.26 1.49 TD[(maps)-486(\()]TJ/F5 9.96 Tf 31.46 0 TD[(\274)-36(;)]TJ/F3 9.96 Tf 10.46 0 TD[(0)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\))-486(to)]TJ/F5 9.96 Tf 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stream
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TD[(r)-322(>)]TJ/F3 9.96 Tf 18.39 0 TD[(0)-343(w)27(e)-342(de\257ne)-344(the)-343(op)-28(en)-343(neigh)27(b)-27(orho)-28(o)-28(d)]TJ/F5 9.96 Tf 156.11 0 TD[(N)]TJ/F7 6.97 Tf 8 -1.5 TD[(r)]TJ/F3 9.96 Tf 4.41 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(A)]TJ/F3 9.96 Tf 7.47 0 TD[(\))-343(as)-343(the)]TJ -329.28 -11.95 TD[(set)]TJ/F5 9.96 Tf 77.45 -23.36 TD[(N)]TJ/F7 6.97 Tf 8.01 -1.49 TD[(r)]TJ/F3 9.96 Tf 4.41 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(A)]TJ/F3 9.96 Tf 7.47 0 TD[(\))-999(:=)]TJ/F10 9.96 Tf 34.31 0 TD[(f)]TJ/F5 9.96 Tf 8.3 0 TD[(y)]TJ/F10 9.96 Tf 8.56 0 TD[(j)]TJ/F5 9.96 Tf 6.08 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x;)-166(y)]TJ/F3 9.96 Tf 15.36 0 TD[(\))]TJ/F5 9.96 Tf 6.64 0 TD[(<)-277(r)27(;)]TJ/F3 9.96 Tf 22.48 0 TD[(for)-332(some)]TJ/F5 9.96 Tf 40.2 0 TD[(x)]TJ/F10 9.96 Tf 8.45 0 TD[(2)]TJ/F5 9.96 Tf 9.41 0 TD[(A)]TJ/F10 9.96 Tf 7.47 0 TD[(g)]TJ/F5 9.96 Tf 4.98 0 TD[(:)]TJ/F3 9.96 Tf -282.51 -23.35 TD[(Think)-333(of)]TJ/F5 9.96 Tf 40.94 0 TD[(N)]TJ/F7 6.97 Tf 8.01 -1.5 TD[(r)]TJ/F3 9.96 Tf 4.41 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(A)]TJ/F3 9.96 Tf 7.47 0 TD[(\))-333(as)-333(the)-334(territorial)-333(b)-28(order)-333(of)]TJ/F5 9.96 Tf 125.25 0 TD[(A)]TJ/F3 9.96 Tf 7.47 0 TD[(.)]TJ/F4 9.96 Tf -197.42 -20.92 TD[(De\257nition)-383(6.6)]TJ/F9 9.96 Tf 0 -11.95 TD[(L)51(et)]TJ/F3 9.96 Tf 18.32 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(X)-22(;)-167(d)]TJ/F3 9.96 Tf 18.09 0 TD[(\))]TJ/F9 9.96 Tf 8.56 0 TD[(b)50(e)-470(a)-472(metric)-471(sp)50(ac)51(e.)-800(The)]TJ/F4 9.96 Tf 110.63 0 TD[(Hausdor\256)-525(distance)]TJ/F5 9.96 Tf 99.62 0 TD[(h)]TJ/F3 9.96 Tf 5.74 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(A)-483(<)-484(B)]TJ/F3 9.96 Tf 32.91 0 TD[(\))]TJ/F9 9.96 Tf 8.57 0 TD[(b)51(etwe)51(en)-470(two)]TJ -310.19 -11.95 TD[(subsets)]TJ/F5 9.96 Tf 33.6 0 TD[(A;)-166(B)]TJ/F10 9.96 Tf 22.71 0 TD[(\275)]TJ/F5 9.96 Tf 10.52 0 TD[(X)]TJ/F9 9.96 Tf 12.59 0 TD[(is)-358(de\257ne)51(d)-357(as)]TJ/F5 9.96 Tf 57.02 0 TD[(h)]TJ/F3 9.96 Tf 5.74 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(A;)-166(B)]TJ/F3 9.96 Tf 19.95 0 TD[(\))-277(:=)-278(inf)]TJ/F10 9.96 Tf 32.04 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(r)]TJ/F3 9.96 Tf 7.53 0 TD[(:)]TJ/F5 9.96 Tf 5.54 0 TD[(A)]TJ/F10 9.96 Tf 10.23 0 TD[(\275)]TJ/F5 9.96 Tf 10.52 0 TD[(N)]TJ/F7 6.97 Tf 8 -1.5 TD[(r)]TJ/F3 9.96 Tf 4.41 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(B)]TJ/F3 9.96 Tf 8.06 0 TD[(\))-357(and)]TJ/F5 9.96 Tf 27.04 0 TD[(B)]TJ/F10 9.96 Tf 10.83 0 TD[(\275)]TJ/F5 9.96 Tf 10.51 0 TD[(N)]TJ/F7 6.97 Tf 8 -1.5 TD[(r)]TJ/F3 9.96 Tf 4.41 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(A)]TJ/F3 9.96 Tf 7.47 0 TD[(\))]TJ/F10 9.96 Tf 3.87 0 TD[(g)]TJ/F9 9.96 Tf 4.98 0 TD[(.)]TJ/F3 9.96 Tf -342.17 -24.35 TD[(The)-345(Hausdor\256)-346(distance)]TJ/F5 9.96 Tf 105.08 0 TD[(h)]TJ/F3 9.96 Tf 9.18 0 TD[(de\257nes)-346(a)-345(metric)-346(on)-346(the)-345(set)-346(of)-345(nonempt)26(y)-344(compact)-346(subsets)]TJ -114.26 -11.95 TD[(of)-333(\()]TJ/F5 9.96 Tf 15.21 0 TD[(X)-23(;)-167(d)]TJ/F3 9.96 Tf 18.1 0 TD[(\),)-332(see)-334([Ca].)-444(Note)-333(that)]TJ/F5 9.96 Tf 48.17 -23.36 TD[(h)]TJ/F3 9.96 Tf 5.74 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(A;)-167(B)]TJ/F3 9.96 Tf 19.96 0 TD[(\))]TJ/F5 9.96 Tf 6.64 0 TD[(<)-277(r)]TJ/F10 9.96 Tf 25.24 0 TD[(,)]TJ/F5 9.96 Tf 19.92 0 TD[(A)]TJ/F10 9.96 Tf 10.23 0 TD[(\275)]TJ/F5 9.96 Tf 10.52 0 TD[(N)]TJ/F7 6.97 Tf 8 -1.49 TD[(r)]TJ/F3 9.96 Tf 4.41 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(B)]TJ/F3 9.96 Tf 8.06 0 TD[(\))]TJ/F10 9.96 Tf 9.4 0 TD[(^)]TJ/F5 9.96 Tf 12.18 0 TD[(B)]TJ/F10 9.96 Tf 10.82 0 TD[(\275)]TJ/F5 9.96 Tf 10.51 0 TD[(N)]TJ/F7 6.97 Tf 8 -1.49 TD[(r)]TJ/F3 9.96 Tf 4.42 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(A)]TJ/F3 9.96 Tf 7.47 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(:)]TJ/F1 11.95 Tf -278.48 -34.41 TD[(6.4.2)-1124(A)-375(compactness)-375(condition.)]TJ/F3 9.96 Tf 0 -22.44 TD[(In)-382(this)-382(section)-383(w)27(e)-381(put)-383(a)-382(compactness)-383(condition)-382(on)-383(the)-382(con\257guration)-383(space)-382(of)-383(data)]TJ 0 -11.95 TD[(sets.)-415(It)-248(consists)-249(of)-248(t)27(w)28(o)-247(ingredien)27(ts.)-415(Supp)-28(ose)-248(that)]TJ/F10 9.96 Tf 210.55 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(1)]TJ/F5 9.96 Tf 4.47 1.49 TD[(;)-166(:)-167(:)-166(:)-167(;)-167(p)]TJ/F7 6.97 Tf 27.14 -1.49 TD[(n)]TJ/F10 9.96 Tf 5.43 1.49 TD[(g)]TJ/F3 9.96 Tf 7.45 0 TD[(denotes)-247(the)-248(underlying)]TJ -265.03 -11.95 TD[(p)-27(oin)27(t)-333(set)-333(of)-333(some)-334(data)-333(set)]TJ/F5 9.96 Tf 116.09 0 TD[(\260)]TJ/F7 6.97 Tf 5.15 -1.5 TD[(n)]TJ/F10 9.96 Tf 8.19 1.5 TD[(2)]TJ/F6 9.96 Tf 9.41 0 TD[(CD)27(A)]TJ/F7 6.97 Tf 21.99 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(.)-444(First)-334(w)27(e)-332(restrict)-334(the)-333(domain)-333(of)]TJ/F10 9.96 Tf 144.48 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(:)-167(:)-166(:)-167(;)-167(p)]TJ/F7 6.97 Tf 27.14 -1.5 TD[(n)]TJ/F10 9.96 Tf 5.42 1.5 TD[(g)]TJ/F3 9.96 Tf -357.75 -11.95 TD[(to)-363(a)-364(closed)-364(disk)]TJ/F10 9.96 Tf 71.88 0 TD[(U)]TJ/F3 9.96 Tf 7.22 0 TD[(.)-535(Moreo)26(v)28(er,)-370(w)26(e)-363(add)-363(four)-364(camera)-364(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 175.62 0 TD[(c)]TJ/F12 6.97 Tf 4.31 -1.5 TD[(1)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(c)]TJ/F12 6.97 Tf 8.73 -1.5 TD[(2)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(c)]TJ/F12 6.97 Tf 8.74 -1.5 TD[(3)]TJ/F3 9.96 Tf 8.09 1.5 TD[(and)]TJ/F5 9.96 Tf 19.67 0 TD[(c)]TJ/F12 6.97 Tf 4.31 -1.5 TD[(4)]TJ/F3 9.96 Tf 8.09 1.5 TD[(far)-364(a)27(w)28(a)27(y)]TJ -325.6 -11.96 TD[(outside)]TJ/F10 9.96 Tf 33.66 0 TD[(U)]TJ/F3 9.96 Tf 7.22 0 TD[(.)-420(Lemma)-263(6.8)-263(sho)27(ws)-262(that)-262(w)26(e)-261(can)-263(c)27(ho)-27(ose)]TJ/F10 9.96 Tf 168.34 0 TD[(U)]TJ/F3 9.96 Tf 9.84 0 TD[(and)]TJ/F5 9.96 Tf 18.66 0 TD[(c)]TJ/F12 6.97 Tf 4.31 -1.49 TD[(1)]TJ/F5 9.96 Tf 4.47 1.49 TD[(;)-166(c)]TJ/F12 6.97 Tf 8.73 -1.49 TD[(2)]TJ/F5 9.96 Tf 4.47 1.49 TD[(;)-166(c)]TJ/F12 6.97 Tf 8.74 -1.49 TD[(3)]TJ/F3 9.96 Tf 7.08 1.49 TD[(and)]TJ/F5 9.96 Tf 18.67 0 TD[(c)]TJ/F12 6.97 Tf 4.31 -1.49 TD[(4)]TJ/F3 9.96 Tf 7.08 1.49 TD[(in)-262(suc)26(h)-261(a)-263(w)27(a)28(y)]TJ -305.58 -11.95 TD[(that)-392(it)-392(is)-393(guaran)27(teed)-391(that)-393(the)-392(V)82(oronoi)-391(diagram)-393(of)]TJ/F5 9.96 Tf 224 0 TD[(\260)]TJ/F7 6.97 Tf 5.15 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(,)-407(extended)-393(with)]TJ/F5 9.96 Tf 73.02 0 TD[(c)]TJ/F12 6.97 Tf 4.31 -1.49 TD[(1)]TJ/F5 9.96 Tf 4.47 1.49 TD[(;)-166(c)]TJ/F12 6.97 Tf 8.73 -1.49 TD[(2)]TJ/F5 9.96 Tf 4.47 1.49 TD[(;)-166(c)]TJ/F12 6.97 Tf 8.74 -1.49 TD[(3)]TJ/F3 9.96 Tf 8.38 1.49 TD[(and)]TJ/F5 9.96 Tf -346.69 -11.95 TD[(c)]TJ/F12 6.97 Tf 4.31 -1.49 TD[(4)]TJ/F3 9.96 Tf 4.47 1.49 TD[(,)-322(c)27(hanges)-320(inside)-320(some)-320(compact)-320(subset)-321(of)-320(the)-320(plane)-320(only)82(,)-322(pro)27(vided)-319(that)-321(w)27(e)-319(p)-28(erturb)]TJ/F10 9.96 Tf -8.78 -11.95 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(:)-167(:)-166(:)-167(;)-167(p)]TJ/F7 6.97 Tf 27.14 -1.5 TD[(n)]TJ/F10 9.96 Tf 5.42 1.5 TD[(g)]TJ/F3 9.96 Tf 8.3 0 TD[(within)]TJ/F10 9.96 Tf 30.99 0 TD[(U)]TJ/F3 9.96 Tf 7.22 0 TD[(.)]TJ -93.53 -15.38 TD[(F)83(or)]TJ/F10 9.96 Tf 17.87 0 TD[(U)]TJ/F3 9.96 Tf 10.54 0 TD[(w)27(e)-332(c)26(ho)-26(ose)-334(the)-333(unit)-333(disk,)-334(that)-333(is)]TJ/F10 9.96 Tf 139.61 0 TD[(U)]TJ/F3 9.96 Tf 9.99 0 TD[(:=)]TJ/F10 9.96 Tf 13.28 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(x)]TJ/F10 9.96 Tf 8.46 0 TD[(2)]TJ/F13 9.96 Tf 9.4 0 TD[(R)]TJ/F12 6.97 Tf 7.2 3.61 TD[(2)]TJ/F10 9.96 Tf 10.55 -3.61 TD[(j)-611(k)]TJ/F5 9.96 Tf 13.83 0 TD[(x)]TJ/F10 9.96 Tf 5.7 0 TD[(k)-277(\267)]TJ/F3 9.96 Tf 18.25 0 TD[(1)]TJ/F10 9.96 Tf 4.98 0 TD[(g)]TJ/F3 9.96 Tf 4.98 0 TD[(.)]TJ/F4 9.96 Tf -279.62 -20.92 TD[(De\257nition)-383(6.7)]TJ/F9 9.96 Tf 0 -11.95 TD[(L)51(et)]TJ/F5 9.96 Tf 16.88 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.5 TD[(n)]TJ/F10 9.96 Tf 8.19 1.5 TD[(2)]TJ/F6 9.96 Tf 9.4 0 TD[(CD)27(A)]TJ/F7 6.97 Tf 22 -1.5 TD[(n)]TJ/F9 9.96 Tf 8.68 1.5 TD[(b)51(e)-326(a)-327(set)-327(of)-327(data)-326(r)50(epr)51(esenting)]TJ/F5 9.96 Tf 124.4 0 TD[(n)]TJ/F9 9.96 Tf 9.23 0 TD[(gener)50(ators)]TJ/F10 9.96 Tf 48.05 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(p)]TJ/F12 6.97 Tf 5.02 -1.5 TD[(1)]TJ/F5 9.96 Tf 4.46 1.5 TD[(;)-167(:)-166(:)-167(:)-166(;)-167(p)]TJ/F7 6.97 Tf 27.15 -1.5 TD[(n)]TJ/F10 9.96 Tf 5.42 1.5 TD[(g)]TJ/F9 9.96 Tf 8.23 0 TD[(in)]TJ/F10 9.96 Tf 11.91 0 TD[(U)]TJ/F9 9.96 Tf 10.48 0 TD[(and)]TJ/F15 9.96 Tf 19.04 8.07 TD[(\241)]TJ/F7 6.97 Tf 4.56 -3.65 TD[(n)]TJ/F12 6.97 Tf 0.48 -7.86 TD[(2)]TJ/F15 9.96 Tf 4.45 11.51 TD[(\242)]TJ/F9 9.96 Tf -358.17 -20.02 TD[(angles)-357(in)]TJ/F13 9.96 Tf 42.25 0 TD[(R)]TJ/F5 9.96 Tf 7.19 0 TD[(=)]TJ/F3 9.96 Tf 4.98 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(\274)]TJ/F13 9.96 Tf 6.04 0 TD[(Z)]TJ/F9 9.96 Tf 10.2 0 TD[(b)50(etwe)52(en)-357(those)-358(gener)50(ators.)-459(L)50(et)-357(furthermor)51(e)]TJ/F5 9.96 Tf 42.21 -23.26 TD[(c)]TJ/F12 6.97 Tf 4.31 -1.49 TD[(1)]TJ/F3 9.96 Tf 7.23 1.49 TD[(=)-278(\()]TJ/F10 9.96 Tf 14.39 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(N)-53(;)]TJ/F3 9.96 Tf 12.96 0 TD[(0\))]TJ/F5 9.96 Tf 8.85 0 TD[(;)-1000(c)]TJ/F12 6.97 Tf 17.04 -1.49 TD[(2)]TJ/F3 9.96 Tf 7.23 1.49 TD[(=)-278(\(0)]TJ/F5 9.96 Tf 19.37 0 TD[(;)-166(N)]TJ/F3 9.96 Tf 13.51 0 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)]TJ -116.52 -11.95 TD[(c)]TJ/F12 6.97 Tf 4.31 -1.49 TD[(3)]TJ/F3 9.96 Tf 7.23 1.49 TD[(=)-278(\()]TJ/F5 9.96 Tf 14.39 0 TD[(N)-53(;)]TJ/F3 9.96 Tf 12.96 0 TD[(0\))]TJ/F5 9.96 Tf 8.86 0 TD[(;)-1777(c)]TJ/F12 6.97 Tf 24.78 -1.49 TD[(4)]TJ/F3 9.96 Tf 7.23 1.49 TD[(=)-278(\(0)]TJ/F5 9.96 Tf 19.37 0 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F5 9.96 Tf 7.74 0 TD[(N)]TJ/F3 9.96 Tf 9.09 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(:)]TJ/F9 9.96 Tf -242.11 -22.9 TD[(for)-423(some)]TJ/F5 9.96 Tf 42.67 0 TD[(N)]TJ/F10 9.96 Tf 13.04 0 TD[(\300)]TJ/F3 9.96 Tf 13.92 0 TD[(1)]TJ/F9 9.96 Tf 9.19 0 TD[(b)50(e)-422(the)-424(so-c)50(al)-50(le)50(d)]TJ/F4 9.96 Tf 70.95 0 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stream
 0.00 g 0.00 G BT/F6 9.96 Tf -8.5 30.56 TD[(6.5.)-777(Con)27(tin)27(uit)28(y)-332(of)-333(the)-334(V)83(oronoi)-333(map.)]TJ/F3 9.96 Tf 352.77 0 TD[(95)]TJ -352.77 -27.96 TD[(Fix)-333(suc)27(h)]TJ/F5 9.96 Tf 40.31 0 TD[(\262)]TJ/F3 9.96 Tf 7.36 0 TD[(and)-333(call)-333(it)]TJ/F5 9.96 Tf 47.59 0 TD[(\262)]TJ/F12 6.97 Tf 4.04 -1.49 TD[(0)]TJ/F3 9.96 Tf 4.47 1.49 TD[(.)-444(W)83(e)-333(can)-333(\257nd)-333(for)-334(ev)27(ery)]TJ/F5 9.96 Tf 104.08 0 TD[(m)]TJ/F10 9.96 Tf 11.51 0 TD[(2)]TJ/F13 9.96 Tf 9.41 0 TD[(N)]TJ/F3 9.96 Tf 10.51 0 TD[(a)-333(triple)]TJ/F5 9.96 Tf 34.89 0 TD[(t)]TJ/F7 6.97 Tf 3.59 -1.49 TD[(m)]TJ/F5 9.96 Tf -170.51 -18.08 TD[(t)]TJ/F7 6.97 Tf 3.6 -1.5 TD[(m)]TJ/F3 9.96 Tf 17.53 1.5 TD[(:=)-999(\()]TJ/F5 9.96 Tf 24.34 0 TD[(\260)]TJ/F7 6.97 Tf 5.71 4.11 TD[(m)]TJ -0.55 -6.57 TD[(n)]TJ/F5 9.96 Tf 8.12 2.46 TD[(;)-499(x)]TJ/F7 6.97 Tf 13.44 4.11 TD[(m)]TJ/F10 9.96 Tf 10.33 -4.11 TD[(2)]TJ/F5 9.96 Tf 9.41 0 TD[(V)]TJ/F3 9.96 Tf 8.02 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.71 4.11 TD[(m)]TJ -0.55 -6.57 TD[(n)]TJ/F3 9.96 Tf 8.12 2.46 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-500(\264)]TJ/F7 6.97 Tf 13.05 4.11 TD[(m)]TJ -0.36 -6.57 TD[(n)]TJ/F3 9.96 Tf 7.93 2.46 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)]TJ/F3 9.96 Tf 89.55 0 TD[(\(6.5\))]TJ -342.26 -19.58 TD[(suc)27(h)-332(that)-333(Assertion)-334(6.4)-333(is)-333(true.)]TJ/F4 9.96 Tf 0 -15.38 TD[(Step)-383(3.)-383(x)]TJ/F8 6.97 Tf 45.02 3.62 TD[(m)]TJ/F10 9.96 Tf 10.75 -3.62 TD[(2)]TJ/F4 9.96 Tf 9.4 0 TD[(B)]TJ/F8 6.97 Tf 8.15 -1.49 TD[(N)]TJ/F5 9.96 Tf 7.48 1.49 TD[(;)]TJ/F10 9.96 Tf 7.75 0 TD[(8)]TJ/F4 9.96 Tf 5.53 0 TD[(m)]TJ/F3 9.96 Tf 9.55 0 TD[(.)]TJ -103.63 -11.95 TD[(Recall)-454(that)]TJ/F5 9.96 Tf 54.01 0 TD[(B)]TJ/F7 6.97 Tf 7.55 -1.49 TD[(N)]TJ/F3 9.96 Tf 12.08 1.49 TD[(denotes)-454(the)-455(disk)]TJ/F5 9.96 Tf 77.6 0 TD[(B)]TJ/F7 6.97 Tf 7.56 -1.49 TD[(N)]TJ/F3 9.96 Tf 12.33 1.49 TD[(=)]TJ/F10 9.96 Tf 12.52 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(x)]TJ/F10 9.96 Tf 10.47 0 TD[(2)]TJ/F13 9.96 Tf 11.41 0 TD[(R)]TJ/F12 6.97 Tf 7.2 3.61 TD[(2)]TJ/F10 9.96 Tf 8.99 -3.61 TD[(j)]TJ/F5 9.96 Tf 7.29 0 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x;)]TJ/F3 9.96 Tf 10.12 0 TD[(0\))]TJ/F10 9.96 Tf 13.63 0 TD[(\267)]TJ/F5 9.96 Tf 12.52 0 TD[(N)]TJ/F10 9.96 Tf 9.09 0 TD[(g)]TJ/F3 9.96 Tf 4.98 0 TD[(.)-807(Supp)-28(ose)-454(that)]TJ/F5 9.96 Tf -293.39 -11.95 TD[(x)]TJ/F7 6.97 Tf 5.69 3.61 TD[(m)]TJ/F10 9.96 Tf 10.37 -3.61 TD[(62)]TJ/F5 9.96 Tf 9.44 0 TD[(B)]TJ/F7 6.97 Tf 7.56 -1.5 TD[(N)]TJ/F3 9.96 Tf 10.9 1.5 TD[(for)-335(some)]TJ/F5 9.96 Tf 40.24 0 TD[(x)]TJ/F7 6.97 Tf 5.69 3.61 TD[(m)]TJ/F10 9.96 Tf 10.37 -3.61 TD[(2)]TJ/F5 9.96 Tf 9.45 0 TD[(V)]TJ/F3 9.96 Tf 8.02 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.71 3.61 TD[(m)]TJ -0.55 -6.07 TD[(n)]TJ/F3 9.96 Tf 8.12 2.46 TD[(\).)-451(Then)-335(Lemma)-336(6.8)-335(tells)-336(us)-336(that)]TJ/F5 9.96 Tf 144.32 0 TD[(x)]TJ/F7 6.97 Tf 5.69 3.61 TD[(m)]TJ/F10 9.96 Tf 10.37 -3.61 TD[(2)]TJ/F5 9.96 Tf 9.44 0 TD[(V)]TJ/F3 9.96 Tf 8.02 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(\264)]TJ/F7 6.97 Tf 4.94 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(\),)-336(for)-336(all)]TJ/F5 9.96 Tf -326.96 -11.95 TD[(\264)]TJ/F7 6.97 Tf 4.94 -1.5 TD[(n)]TJ/F10 9.96 Tf 8.19 1.5 TD[(2)]TJ/F6 9.96 Tf 9.41 0 TD[(CD)27(A)]TJ/F17 6.97 Tf 21.99 4.34 TD[(U)]TJ/F7 6.97 Tf 0 -6.81 TD[(n)]TJ/F3 9.96 Tf 6.21 2.47 TD[(.)-444(So)-333(Assertion)-333(6.4)-334(can)-333(nev)27(er)-333(b)-27(e)-334(true.)]TJ/F4 9.96 Tf -50.74 -15.39 TD[(Step)-383(4.)-383(Remarks)-383(on)-384(compactness.)]TJ/F5 9.96 Tf 0 -11.95 TD[(\260)]TJ/F7 6.97 Tf 5.15 -1.49 TD[(n)]TJ/F3 9.96 Tf 8.75 1.49 TD[(and)]TJ/F5 9.96 Tf 19.36 0 TD[(\264)]TJ/F7 6.97 Tf 4.95 -1.49 TD[(n)]TJ/F3 9.96 Tf 8.74 1.49 TD[(b)-27(oth)-334(liv)27(e)-332(in)-333(the)-334(compact)-333(set)]TJ/F10 9.96 Tf 56 -21.58 TD[(U)]TJ/F7 6.97 Tf 7.23 4.11 TD[(n)]TJ/F10 9.96 Tf 7.63 -4.11 TD[(\243)-222(f)]TJ/F5 9.96 Tf 14.94 0 TD[(c)]TJ/F12 6.97 Tf 4.31 -1.5 TD[(1)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(c)]TJ/F12 6.97 Tf 8.74 -1.5 TD[(2)]TJ/F5 9.96 Tf 4.46 1.5 TD[(;)-167(c)]TJ/F12 6.97 Tf 8.74 -1.5 TD[(3)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(c)]TJ/F12 6.97 Tf 8.74 -1.5 TD[(4)]TJ/F10 9.96 Tf 4.46 1.5 TD[(g)-222(\243)]TJ/F3 9.96 Tf 17.16 0 TD[(\()]TJ/F13 9.96 Tf 3.87 0 TD[(R)]TJ/F5 9.96 Tf 7.19 0 TD[(=)]TJ/F3 9.96 Tf 4.98 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(\274)]TJ/F13 9.96 Tf 6.04 0 TD[(Z)]TJ/F3 9.96 Tf 6.64 0 TD[(\))]TJ 3.87 3.56 TD[(\()]TJ/F14 4.98 Tf 3.87 4.03 TD[(n)]TJ/F16 4.98 Tf 4.39 0 TD[(+4)]TJ 0.37 -5.69 TD[(2)]TJ/F3 9.96 Tf 8.14 1.66 TD[(\))]TJ/F5 9.96 Tf 4.37 -3.56 TD[(:)]TJ/F3 9.96 Tf -257.01 -19.58 TD[(W)83(e)-383(ha)27(v)28(e)-383(pro)27(v)28(ed)-383(in)-384(Lemma)-384(6.10)-383(that)-384(the)-384(set)]TJ/F10 9.96 Tf 199.51 0 TD[(f)]TJ/F3 9.96 Tf 4.98 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.49 TD[(n)]TJ/F5 9.96 Tf 5.42 1.49 TD[(;)-166(x)]TJ/F3 9.96 Tf 10.12 0 TD[(\))]TJ/F10 9.96 Tf 7.7 0 TD[(j)]TJ/F5 9.96 Tf 6.58 0 TD[(x)]TJ/F10 9.96 Tf 9.3 0 TD[(2)]TJ/F5 9.96 Tf 10.24 0 TD[(V)]TJ/F3 9.96 Tf 8.03 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\))]TJ/F10 9.96 Tf 3.87 0 TD[(g)]TJ/F3 9.96 Tf 8.8 0 TD[(is)-383(closed.)-596(This)]TJ -298.03 -11.95 TD[(means)-373(that)-375(w)27(e)-373(get)-374(a)-374(sequence)-374(\()]TJ/F5 9.96 Tf 139.22 0 TD[(t)]TJ/F7 6.97 Tf 3.59 -1.49 TD[(m)]TJ/F3 9.96 Tf 7.57 1.49 TD[(\))-374(of)-374(triples)-374(of)-374(the)-374(form)-374(\(6.5\))-374(that)-374(liv)26(e)-373(on)-374(a)-374(com-)]TJ -150.38 -11.95 TD[(pact)-394(set.)-628(So,)-410(\()]TJ/F5 9.96 Tf 65.23 0 TD[(t)]TJ/F7 6.97 Tf 3.59 -1.5 TD[(m)]TJ/F3 9.96 Tf 7.57 1.5 TD[(\))-394(has)-394(some)-395(con)27(v)28(ergen)28(t)-394(subsequence)]TJ/F5 9.96 Tf 159.06 0 TD[(t)]TJ/F7 6.97 Tf 3.59 -1.5 TD[(m)]TJ/F3 9.96 Tf 7.57 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(k)]TJ/F3 9.96 Tf 5.5 0 TD[(\))-394(that)-394(con)26(v)28(erges)-393(to,)-410(sa)27(y)83(,)]TJ -255.98 -11.95 TD[(\()-36(~)]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.5 TD[(n)]TJ/F5 9.96 Tf 5.42 1.5 TD[(;)]TJ/F3 9.96 Tf 5.06 0 TD[(~)]TJ/F5 9.96 Tf -0.63 0 TD[(x;)]TJ/F3 9.96 Tf 10.83 0 TD[(~)]TJ/F5 9.96 Tf -0.71 0 TD[(\264)]TJ/F7 6.97 Tf 4.94 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(\).)-444(Note)-333(that)-397(~)]TJ/F5 9.96 Tf 56.72 0 TD[(x)]TJ/F10 9.96 Tf 8.46 0 TD[(2)]TJ/F5 9.96 Tf 9.4 0 TD[(V)]TJ/F3 9.96 Tf 8.03 0 TD[(\()-36(~)]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(\).)]TJ/F4 9.96 Tf -136.42 -15.39 TD[(Step)-383(5.)-894(A)-383(con)30(tradiction)-382(b)31(y)-382(com)31(bining)-383(Assertion)-383(6.4)-383(and)-384(Theorem)-383(6.1.)]TJ/F3 9.96 Tf 0 -11.95 TD[(Because)-333(of)-333(con)27(v)28(ergence,)]TJ/F5 9.96 Tf 107.29 0 TD[(V)]TJ/F3 9.96 Tf 8.02 0 TD[(\()-36(~)]TJ/F5 9.96 Tf 3.88 0 TD[(\260)]TJ/F7 6.97 Tf 5.15 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\))-278(=)]TJ/F5 9.96 Tf 17.16 0 TD[(V)]TJ/F3 9.96 Tf 8.02 0 TD[(\()-71(~)]TJ/F5 9.96 Tf 3.87 0 TD[(\264)]TJ/F7 6.97 Tf 4.95 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\),)-333(so)-397(~)]TJ/F5 9.96 Tf 22.19 0 TD[(x)]TJ/F10 9.96 Tf 8.46 0 TD[(2)]TJ/F5 9.96 Tf 9.4 0 TD[(V)]TJ/F3 9.96 Tf 8.03 0 TD[(\()-71(~)]TJ/F5 9.96 Tf 3.87 0 TD[(\264)]TJ/F7 6.97 Tf 4.95 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\).)-444(Apply)-333(Theorem)-333(6.1)-334(with)]TJ/F10 9.96 Tf -216.56 -21.48 TD[(\262)]TJ/F3 9.96 Tf 10.59 0 TD[(~)]TJ/F5 9.96 Tf -0.63 0 TD[(x)]TJ/F10 9.96 Tf 8.46 0 TD[(2)]TJ/F5 9.96 Tf 9.4 0 TD[(V)]TJ/F3 9.96 Tf 8.03 0 TD[(\()-71(~)]TJ/F5 9.96 Tf 3.87 0 TD[(\264)]TJ/F7 6.97 Tf 4.95 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\),)]TJ/F10 9.96 Tf -50.09 -18.98 TD[(\262)]TJ/F5 9.96 Tf 9.96 0 TD[(\262)]TJ/F3 9.96 Tf 10.13 0 TD[(=)]TJ/F12 6.97 Tf 15.03 3.92 TD[(1)]TJ ET 0.4 w 41.56 -257.44 m 45.53 -257.44 l S BT 41.56 -263.37 TD[(3)]TJ/F5 9.96 Tf 5.16 3.44 TD[(\262)]TJ/F12 6.97 Tf 4.04 -1.5 TD[(0)]TJ/F3 9.96 Tf 4.47 1.5 TD[(.)]TJ -63.73 -21.48 TD[(The)-333(theorem)-333(giv)27(es)-333(us)-333(a)]TJ/F5 9.96 Tf 104.72 0 TD[(\261)]TJ/F12 6.97 Tf 4.42 -1.5 TD[(0)]TJ/F3 9.96 Tf 7.79 1.5 TD[(suc)27(h)-332(that)]TJ/F5 9.96 Tf -27.06 -19.58 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\()-72(~)]TJ/F5 9.96 Tf 3.88 0 TD[(\264)]TJ/F7 6.97 Tf 4.94 -1.49 TD[(n)]TJ/F5 9.96 Tf 5.43 1.49 TD[(;)-166(\265)]TJ/F7 6.97 Tf 9.1 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\))]TJ/F5 9.96 Tf 9.96 0 TD[(<)-610(\261)]TJ/F12 6.97 Tf 18.26 -1.49 TD[(0)]TJ/F10 9.96 Tf 14.43 1.49 TD[(\))]TJ/F5 9.96 Tf 19.92 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(V)]TJ/F3 9.96 Tf 8.03 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\265)]TJ/F7 6.97 Tf 4.68 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)]TJ/F3 9.96 Tf 5.06 0 TD[(~)]TJ/F5 9.96 Tf -0.63 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))]TJ/F5 9.96 Tf 9.96 0 TD[(<)]TJ/F12 6.97 Tf 15.03 3.93 TD[(1)]TJ ET 0.4 w 247.92 -298.5 m 251.89 -298.5 l S BT 247.92 -304.42 TD[(3)]TJ/F5 9.96 Tf 5.16 3.43 TD[(\262)]TJ/F12 6.97 Tf 4.05 -1.49 TD[(0)]TJ/F5 9.96 Tf 4.46 1.49 TD[(:)]TJ/F3 9.96 Tf 72.17 0 TD[(\(6.6\))]TJ -342.26 -19.57 TD[(Cho)-27(ose)]TJ/F5 9.96 Tf 34.64 0 TD[(m)]TJ/F3 9.96 Tf 12.06 0 TD[(so)-333(big)-333(that)-334(the)-333(follo)27(wing)-333(condition)-333(hold:)]TJ/F5 9.96 Tf 31.56 -19.57 TD[(d)]TJ/F3 9.96 Tf 5.19 0 TD[(\()-332(\()]TJ/F5 9.96 Tf 11.06 0 TD[(\260)]TJ/F7 6.97 Tf 5.71 4.11 TD[(m)]TJ -0.55 -6.58 TD[(n)]TJ/F5 9.96 Tf 8.12 2.47 TD[(;)-166(x)]TJ/F7 6.97 Tf 10.12 4.11 TD[(m)]TJ/F5 9.96 Tf 7.56 -4.11 TD[(;)-166(\264)]TJ/F7 6.97 Tf 9.73 4.11 TD[(m)]TJ -0.36 -6.58 TD[(n)]TJ/F3 9.96 Tf 7.93 2.47 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(\()-36(~)]TJ/F5 9.96 Tf 3.87 0 TD[(\260)]TJ/F7 6.97 Tf 5.16 -1.5 TD[(n)]TJ/F5 9.96 Tf 5.42 1.5 TD[(;)]TJ/F3 9.96 Tf 5.06 0 TD[(~)]TJ/F5 9.96 Tf -0.64 0 TD[(x;)]TJ/F3 9.96 Tf 10.84 0 TD[(~)]TJ/F5 9.96 Tf -0.72 0 TD[(\264)]TJ/F7 6.97 Tf 4.95 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(\))-333(\))]TJ/F5 9.96 Tf 21.03 0 TD[(<)]TJ/F3 9.96 Tf 17.7 0 TD[(min\()]TJ/F5 9.96 Tf 20.48 0 TD[(\261)]TJ/F12 6.97 Tf 4.42 -1.5 TD[(0)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)]TJ/F12 6.97 Tf 5.62 3.92 TD[(1)]TJ ET 0.4 w 255.65 -337.64 m 259.62 -337.64 l S BT 255.65 -343.57 TD[(3)]TJ/F5 9.96 Tf 5.17 3.44 TD[(\262)]TJ/F12 6.97 Tf 4.04 -1.5 TD[(0)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(:)]TJ/F3 9.96 Tf 60.56 0 TD[(\(6.7\))]TJ -342.26 -19.58 TD[(W)83(e)-332(sho)26(w)-332(that)-333(this)-334(leads)-333(to)-333(a)-334(con)27(tradiction)-332(on)]TJ/F5 9.96 Tf 202.71 0 TD[(d)]TJ/F3 9.96 Tf 5.18 0 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(x)]TJ/F7 6.97 Tf 5.69 3.62 TD[(m)]TJ/F5 9.96 Tf 7.57 -3.62 TD[(;)-166(V)]TJ/F3 9.96 Tf 12.45 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(\264)]TJ/F7 6.97 Tf 5.3 3.62 TD[(m)]TJ -0.36 -6.08 TD[(n)]TJ/F3 9.96 Tf 7.93 2.46 TD[(\)\).)]TJ -244.7 -11.95 TD[(\(i\))-833(The)-334(sequence)]TJ/F5 9.96 Tf 80.57 0 TD[(t)]TJ/F7 6.97 Tf 3.6 -1.49 TD[(m)]TJ/F3 9.96 Tf 10.88 1.49 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TD[(b)-28(et)27(w)28(een)-304(the)-304(line)-304(segmen)27(ts.)-434(In)-304(this)-305(w)27(a)28(y)-304(ev)27(ery)-303(ho)-28(ok)-304(has)-304(t)26(w)28(o)-303(repre-)]TJ -80.17 -13.4 TD[(sen)27(tativ)28(es.)-433(One)-303(with)-303(a)-304(p)-27(ositiv)26(e)-302(ratio)]TJ/F5 9.96 Tf 160.71 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.52 -6.2 TD[(ij)]TJ/F3 9.96 Tf 12.62 2.59 TD[(and)-303(one)-303(with)-303(a)-303(negativ)27(e)-303(`ratio')]TJ/F5 9.96 Tf 135.45 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.53 -6.2 TD[(ij)]TJ/F3 9.96 Tf 9.61 2.59 TD[(.)-434(In)-303(the)]TJ -329.66 -13.4 TD[(latter)-338(case)-338(w)27(e)-337(just)-338(add)]TJ/F5 9.96 Tf 102.19 0 TD[(\274)]TJ/F3 9.96 Tf 9.41 0 TD[(to)-337(the)-338(ho)-28(ok)-338(angle)]TJ/F5 9.96 Tf 79.87 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 3.61 TD[(ik)]TJ -0.04 -6.2 TD[(ij)]TJ/F3 9.96 Tf 9.12 2.59 TD[(.)-458(These)-338(t)26(w)28(o)-337(distinct)-338(represen)26(tativ)28(es)]TJ -206.96 -11.95 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Tf 4.19 1.49 TD[(.)-777(In)-444(fact,)-472(one)-445(can)-444(pro)27(v)28(e)-444(that)-444(the)-444(set)]TJ/F10 9.96 Tf 172.15 0 TD[(C)]TJ/F3 9.96 Tf 5.83 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))-444(consisting)]TJ -311.72 -11.95 TD[(basically)-305(of)-305(all)-306(sets)]TJ/F5 9.96 Tf 84.27 0 TD[(C)]TJ/F7 6.97 Tf 7.11 -1.5 TD[(ij)]TJ/F3 9.96 Tf 9.79 1.5 TD[(=)]TJ/F10 9.96 Tf 10.51 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(k)]TJ/F10 9.96 Tf 8.54 0 TD[(j)]TJ/F5 9.96 Tf 5.81 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.53 -6.2 TD[(ij)]TJ/F10 9.96 Tf 12.37 2.59 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)-277(0)]TJ/F10 9.96 Tf 15.49 0 TD[(g)-166([)-166(f)]TJ/F5 9.96 Tf 19.92 0 TD[(i;)-166(j)]TJ/F10 9.96 Tf 12.52 0 TD[(g)]TJ/F3 9.96 Tf 8.03 0 TD[(de\257nes)-304(a)-306(nest)-305(on)]TJ/F10 9.96 Tf 74.8 0 TD[(f)]TJ/F3 9.96 Tf 4.98 0 TD[(1)]TJ/F5 9.96 Tf 4.98 0 TD[(;)-166(:)-167(:)-166(:)-167(;)-167(n)]TJ/F10 9.96 Tf 28.11 0 TD[(g)]TJ/F3 9.96 Tf 4.98 0 TD[(.)-434(So)]TJ/F10 9.96 Tf 20.65 0 TD[(C)]TJ/F3 9.96 Tf 5.83 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))]TJ -358.86 -11.95 TD[(is)-374(the)-373(nest)-374(that)-374(corresp)-27(onds)-374(to)]TJ/F5 9.96 Tf 139.09 0 TD[(x)]TJ/F10 9.96 Tf 9.13 0 TD[(2)]TJ/F6 9.96 Tf 10.07 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(.)-566(F)83(or)-373(ev)27(ery)-373(cluster)-374(in)]TJ/F10 9.96 Tf 97.99 0 TD[(C)]TJ/F3 9.96 Tf 5.83 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))-374(with)-373(at)-374(least)]TJ -299.5 -11.95 TD[(t)27(w)28(o)-333(elemen)27(ts)-332(w)27(e)-333(de\257ne)-333(a)-333(screen)-334(as)-333(a)-333(cop)26(y)-332(of)-333(the)-334(plane.)]TJ/F1 11.95 Tf 0 -31.49 TD[(7.2.4)-1125(F)93(actorizing)]TJ/F22 11.95 Tf 110.5 0 TD[(XAH)]TJ/F24 7.97 Tf 26.31 -1.79 TD[(n)]TJ/F1 11.95 Tf 5.64 1.79 TD[(.)]TJ/F3 9.96 Tf -142.45 -21.85 TD[(Fix)-271(some)]TJ/F5 9.96 Tf 41.57 0 TD[(x)]TJ/F10 9.96 Tf 8.46 0 TD[(2)]TJ/F6 9.96 Tf 9.41 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(.)-423(By)-272(analyzing)-272(the)]TJ/F5 9.96 Tf 82.47 0 TD[(C)]TJ/F7 6.97 Tf 7.12 -1.49 TD[(ij)]TJ/F3 9.96 Tf 9.72 1.49 TD[(as)-271(explained)-272(ab)-28(o)27(v)28(e,)-283(w)27(e)-271(asso)-28(ciate)-271(a)-272(family)]TJ -186.58 -11.95 TD[(of)-336(screens)-336(with)]TJ/F5 9.96 Tf 68 0 TD[(x)]TJ/F3 9.96 Tf 9.04 0 TD[(denoted)-335(b)27(y)]TJ/F4 9.96 Tf 51.51 0 TD[(x)]TJ/F3 9.96 Tf 6.04 0 TD[(-)]TJ/F4 9.96 Tf 3.32 0 TD[(screens)]TJ/F3 9.96 Tf 35.71 0 TD[(.)-451(Our)-336(next)-336(goal)-336(is)-336(to)-336(\257ll)-336(the)]TJ/F5 9.96 Tf 125.11 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-screens.)-452(The)]TJ -304.42 -11.95 TD[(main)-239(idea)-239(of)-240(w)27(orking)-238(with)-240(screens)-239(is)-239(as)-239(follo)26(ws:)-396(the)-239(site)-240(set)]TJ/F5 9.96 Tf 250.57 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(:)-167(:)-166(:)-167(;)-167(p)]TJ/F7 6.97 Tf 27.14 -1.5 TD[(n)]TJ/F3 9.96 Tf 7.81 1.5 TD[(that)-239(w)27(e)-238(think)-239(of)]TJ -295 -11.95 TD[(as)-346(corresp)-27(onding)-346(to)-346(some)-346(degenerate)-346(con\257guration)]TJ/F5 9.96 Tf 224.29 0 TD[(q)]TJ/F10 9.96 Tf 7.78 0 TD[(2)]TJ/F6 9.96 Tf 9.61 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(,)-349(should)-346(b)-27(e)-346(separated)]TJ -269.51 -11.95 TD[(completely)83(,)-435(somewhere)-415(in)-415(the)-415(hierarc)27(h)28(y)-414(of)]TJ/F5 9.96 Tf 191.14 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-screens.)-689(This)-415(puts)-415(a)-415(requiremen)27(t)-414(on)]TJ -196.83 -11.96 TD[(those)-293(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 55.19 0 TD[(q)]TJ/F10 9.96 Tf 7.57 0 TD[(2)]TJ/F6 9.96 Tf 9.41 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.49 TD[(n)]TJ/F3 9.96 Tf 8.34 1.49 TD[(that)-292(w)26(e)-292(can)-293(use)-292(to)-293(\257ll)-293(the)]TJ/F5 9.96 Tf 112.61 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-screens)-292(with:)-425(the)-293(p)-27(oin)26(t)]TJ/F5 9.96 Tf 105.52 0 TD[(q)]TJ/F3 9.96 Tf 7.72 0 TD[(should)]TJ -334.46 -11.95 TD[(not)-334(b)-28(e)-335(more)-334(nested)-334(than)]TJ/F5 9.96 Tf 110.53 0 TD[(x)]TJ/F3 9.96 Tf 9.03 0 TD[(itself,)-334(in)-334(the)-335(follo)27(wing)-333(sense:)-447(if)]TJ/F5 9.96 Tf 136.36 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.62 TD[(ik)]TJ -0.52 -6.21 TD[(ij)]TJ/F3 9.96 Tf 9.6 2.59 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(\))]TJ/F10 9.96 Tf 6.66 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)-279(0)]TJ/F5 9.96 Tf 15.51 0 TD[(;)]TJ/F10 9.96 Tf 4.42 0 TD[(1)]TJ/F3 9.96 Tf 9.96 0 TD[(,)-335(then)-334(also)]TJ/F5 9.96 Tf -317.28 -13.4 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.62 TD[(ik)]TJ -0.52 -6.21 TD[(ij)]TJ/F3 9.96 Tf 9.6 2.59 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))]TJ/F10 9.96 Tf 7.3 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)-344(0)]TJ/F5 9.96 Tf 16.16 0 TD[(;)]TJ/F10 9.96 Tf 4.42 0 TD[(1)]TJ/F3 9.96 Tf 9.96 0 TD[(.)-564(Another)-374(w)27(a)28(y)-372(to)-374(put)-373(this:)-524(w)26(e)-372(are)-373(not)-374(allo)27(w)28(ed)-372(to)-374(mo)27(v)28(e)-372(do)26(wn)-372(in)-373(the)]TJ -61.76 -13.41 TD[(strati\257cation)-314(with)-313(resp)-28(ect)-314(to)-314(the)-314(coincidence)-313(of)-314(sites.)-438(W)82(e)-313(do)-313(not)-314(need)-314(all)]TJ/F15 9.96 Tf 318.26 8.07 TD[(\241)]TJ/F7 6.97 Tf 4.56 -3.65 TD[(n)]TJ/F12 6.97 Tf 0.48 -7.85 TD[(2)]TJ/F15 9.96 Tf 4.44 11.5 TD[(\242)]TJ/F3 9.96 Tf 6.39 -8.07 TD[(+)-183(6)]TJ/F15 9.96 Tf 14.55 8.07 TD[(\241)]TJ/F7 6.97 Tf 4.57 -3.65 TD[(n)]TJ/F12 6.97 Tf 0.48 -7.85 TD[(3)]TJ/F15 9.96 Tf 4.44 11.5 TD[(\242)]TJ/F3 9.96 Tf -358.17 -20.02 TD[(data)-333(elemen)27(ts)]TJ 48.91 -21.99 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.5 TD[(ij)]TJ/F3 9.96 Tf 7.01 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\)\))]TJ/F12 6.97 Tf 7.75 -1.5 TD[(1)]TJ/F17 6.97 Tf 3.97 0 TD[(\267)]TJ/F7 6.97 Tf 6.22 0 TD[(i<j)]TJ/F17 6.97 Tf 12.74 0 TD[(\267)]TJ/F7 6.97 Tf 6.23 0 TD[(n)]TJ/F5 9.96 Tf 5.42 1.5 TD[(;)-166(h)]TJ/F7 6.97 Tf 10.16 4.11 TD[(ik)]TJ 0 -6.57 TD[(ij)]TJ/F3 9.96 Tf 9.08 2.46 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\)\))]TJ/F5 9.96 Tf 7.75 0 TD[(;)-2166(i;)-166(j)-2(;)-167(k)-31(;)]TJ/F3 9.96 Tf 53.99 0 TD[(pairwise)-333(distinct)-333(indices)]TJ/F5 9.96 Tf 104.22 0 TD[(;)]TJ/F3 9.96 Tf -311.06 -21.99 TD[(for)-377(\257lling)-377(the)]TJ/F5 9.96 Tf 61.38 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-screens)-377(with)-377(sites)]TJ/F5 9.96 Tf 83.45 0 TD[(p)]TJ/F12 6.97 Tf 5.02 -1.5 TD[(1)]TJ/F3 9.96 Tf 4.46 1.5 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-167(:)-166(:)-167(:)-167(;)-166(p)]TJ/F7 6.97 Tf 27.15 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\),)-387(giv)26(en)-376(some)-377(suitable)]TJ/F5 9.96 Tf 99.91 0 TD[(q)]TJ/F10 9.96 Tf 8.29 0 TD[(2)]TJ/F6 9.96 Tf 10.14 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(.)]TJ -359.97 -11.96 TD[(W)83(e)-399(just)-400(need)-400(enough)-400(data)-400(elemen)26(ts)-399(to)-400(pinp)-27(oin)26(t)-399(eac)27(h)-399(site)-400(once.)-644(By)-400(exploiting)-400(the)]TJ 0 -11.95 TD[(nested)-303(structure)-303(of)]TJ/F5 9.96 Tf 84.2 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(,)-308(w)26(e)-301(can)-303(a)26(v)28(oid)-302(bad)-303(c)27(hoices)-302(in)-303(pic)27(king)-302(the)-303(data)-303(elemen)27(ts.)-433(W)82(e)-302(do)]TJ -89.89 -11.95 TD[(not)-301(w)27(an)28(t)-300(to)-301(b)-28(e)-300(confron)26(ted)-300(with)-300(legs)-301(of)-301(length)-301(0)]TJ/F10 9.96 Tf 204.58 0 TD[(\242)-157(1)]TJ/F3 9.96 Tf 17.29 0 TD[(for)-300(example.)-434(These)-301(prerequisites)]TJ -221.87 -11.95 TD[(result)-447(in)-448(a)-447(factor)]TJ/F4 9.96 Tf 80.74 0 TD[(Dom)]TJ/F7 6.97 Tf 24.06 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))-447(of)-448(data)-447(elemen)27(ts)-447(of)]TJ/F6 9.96 Tf 98.97 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.5 TD[(n)]TJ/F3 9.96 Tf 9.88 1.5 TD[(that)-447(are)-447(b)-28(oth)-448(suited)-447(and)]TJ -251.04 -11.95 TD[(enough)-321(to)-321(\257ll)-321(the)]TJ/F5 9.96 Tf 77.54 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-screens,)-323(giv)27(en)-320(some)-321(suitable)]TJ/F5 9.96 Tf 127.6 0 TD[(q)]TJ/F10 9.96 Tf 7.57 0 TD[(2)]TJ/F6 9.96 Tf 9.41 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(.)-440(Note)-321(that)-321(the)-321(c)26(hoice)-320(of)]TJ -255.64 -11.95 TD[(the)-373(data)-374(elemen)27(ts)-373(dep)-27(ends)-374(on)]TJ/F5 9.96 Tf 134.91 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(,)-383(although)-373(w)27(e)-373(use)-373(of)-374(course)-374(the)-373(data)-374(elemen)27(ts)-372(of)]TJ/F5 9.96 Tf 217.32 0 TD[(q)]TJ/F3 9.96 Tf -357.93 -11.96 TD[(itself)-333(in)-333(order)-334(to)-333(\257ll)-333(the)]TJ/F5 9.96 Tf 105.52 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(-screens)-332(with)-334(sites)]TJ/F5 9.96 Tf 82.14 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)-166(:)-166(:)-167(:)-167(;)-166(p)]TJ/F7 6.97 Tf 27.14 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\).)]TJ/F1 11.95 Tf -256.63 -31.48 TD[(7.2.5)-1125(The)-375(ho)-31(ok)30(ed)-374(tree.)]TJ/F3 9.96 Tf 0 -21.85 TD[(Again)-327(b)27(y)-326(using)-327(the)-328(nested)-327(structure)-327(of)-327(our)-327(\257xed)]TJ/F5 9.96 Tf 212.45 0 TD[(x)]TJ/F10 9.96 Tf 8.46 0 TD[(2)]TJ/F6 9.96 Tf 9.41 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(,)-328(w)27(e)-326(can)-327(de\257ne)-328(a)-327(partial)]TJ -258.15 -11.95 TD[(order)-337(on)-337(the)-337(lab)-28(els)-337(1)]TJ/F5 9.96 Tf 90.18 0 TD[(;)-166(:)-167(:)-167(:)-166(;)-167(n)]TJ/F3 9.96 Tf 28.11 0 TD[(.)-456(This)-337(partial)-337(order)-337(tells)-337(in)-337(whic)26(h)-336(order)-337(exactly)-337(w)27(e)-336(ha)26(v)28(e)]TJ -118.29 -11.95 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Tf 10.83 3.61 TD[(ik)]TJ -0.03 -6.2 TD[(ij)]TJ/F3 9.96 Tf 11.32 2.59 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\274)]TJ/F3 9.96 Tf 6.04 0 TD[(\))]TJ/F10 9.96 Tf 3.87 0 TD[(g)]TJ/F3 9.96 Tf 4.98 0 TD[(;)]TJ -218.72 -14.11 TD[(\(iii\))]TJ/F5 9.96 Tf 24.34 0 TD[(c)]TJ/F17 6.97 Tf 4.31 4.26 TD[(\241)]TJ/F12 6.97 Tf 6.23 0 TD[(1)]TJ/F7 6.97 Tf -6.23 -7.26 TD[(ij)-58(k)]TJ/F3 9.96 Tf 11.42 3 TD[(\()-333([\()]TJ/F10 9.96 Tf 13.83 0 TD[(\2411)]TJ/F5 9.96 Tf 17.71 0 TD[(;)-166(\256)]TJ/F7 6.97 Tf 10.83 3.61 TD[(ik)]TJ -0.03 -6.2 TD[(ij)]TJ/F3 9.96 Tf 9.11 2.59 TD[(\)])-333(\))-278(=)]TJ/F10 9.96 Tf 27.11 0 TD[(f)]TJ/F3 9.96 Tf 4.98 0 TD[(\()]TJ/F10 9.96 Tf 3.88 0 TD[(1)]TJ/F5 9.96 Tf 9.96 0 TD[(;)-166(\256)]TJ/F7 6.97 Tf 10.83 3.61 TD[(ik)]TJ -0.03 -6.2 TD[(ij)]TJ/F3 9.96 Tf 9.11 2.59 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(\()]TJ/F10 9.96 Tf 3.87 0 TD[(1)]TJ/F5 9.96 Tf 9.96 0 TD[(;)-167(\256)]TJ/F7 6.97 Tf 10.84 3.61 TD[(ik)]TJ -0.04 -6.2 TD[(ij)]TJ/F3 9.96 Tf 11.33 2.59 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\274)]TJ/F3 9.96 Tf 6.04 0 TD[(\))]TJ/F10 9.96 Tf 3.87 0 TD[(g)]TJ/F3 9.96 Tf 4.98 0 TD[(;)]TJ -226.2 -14.11 TD[(\(iv\))]TJ/F5 9.96 Tf 24.07 0 TD[(c)]TJ/F17 6.97 Tf 4.31 4.26 TD[(\241)]TJ/F12 6.97 Tf 6.23 0 TD[(1)]TJ/F7 6.97 Tf -6.23 -7.26 TD[(ij)-58(k)]TJ/F3 9.96 Tf 11.42 3 TD[(\()-333([\()]TJ/F5 9.96 Tf 13.83 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.52 -6.2 TD[(ij)]TJ/F5 9.96 Tf 9.6 2.59 TD[(;)-166(\256)]TJ/F7 6.97 Tf 10.83 3.61 TD[(ik)]TJ -0.03 -6.2 TD[(ij)]TJ/F3 9.96 Tf 9.11 2.59 TD[(\)])-333(\))-278(=)-278(\()]TJ/F5 9.96 Tf 30.99 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.53 -6.2 TD[(ij)]TJ/F5 9.96 Tf 9.61 2.59 TD[(;)-166(\256)]TJ/F7 6.97 Tf 10.83 3.61 TD[(ik)]TJ -0.03 -6.2 TD[(ij)]TJ/F3 9.96 Tf 9.11 2.59 TD[(\),)-333(if)-333(0)]TJ/F5 9.96 Tf 26.84 0 TD[(<)-277(\257)]TJ/F7 6.97 Tf 16.67 3.61 TD[(ik)]TJ -0.53 -6.2 TD[(ij)]TJ/F5 9.96 Tf 12.37 2.59 TD[(<)]TJ/F10 9.96 Tf 10.52 0 TD[(1)]TJ/F3 9.96 Tf 9.96 0 TD[(;)]TJ -227.98 -14.11 TD[(\(v\))]TJ/F5 9.96 Tf 21.3 0 TD[(c)]TJ/F17 6.97 Tf 4.31 4.26 TD[(\241)]TJ/F12 6.97 Tf 6.23 0 TD[(1)]TJ/F7 6.97 Tf -6.23 -7.26 TD[(ij)-58(k)]TJ/F3 9.96 Tf 11.42 3 TD[(\()-333([\()]TJ/F5 9.96 Tf 13.83 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.52 -6.2 TD[(ij)]TJ/F5 9.96 Tf 9.6 2.59 TD[(;)-166(\256)]TJ/F7 6.97 Tf 10.83 3.61 TD[(ik)]TJ -0.03 -6.2 TD[(ij)]TJ/F3 9.96 Tf 9.11 2.59 TD[(\)])-333(\))-278(=)-278(\()]TJ/F10 9.96 Tf 30.99 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.53 -6.2 TD[(ij)]TJ/F5 9.96 Tf 9.6 2.59 TD[(;)-167(\256)]TJ/F7 6.97 Tf 10.84 3.61 TD[(ik)]TJ -0.04 -6.2 TD[(ij)]TJ/F3 9.96 Tf 11.33 2.59 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\274)]TJ/F3 9.96 Tf 6.04 0 TD[(\),)-332(if)]TJ/F10 9.96 Tf 19.08 0 TD[(\2411)]TJ/F5 9.96 Tf 20.48 0 TD[(<)-277(\257)]TJ/F7 6.97 Tf 16.67 3.61 TD[(ik)]TJ -0.53 -6.2 TD[(ij)]TJ/F5 9.96 Tf 12.38 2.59 TD[(<)]TJ/F3 9.96 Tf 10.51 0 TD[(0.)]TJ/F18 9.96 Tf 91.25 0 TD[(\245)]TJ/F4 9.96 Tf -354.99 -20.92 TD[(Remark)-383(7.7)]TJ/F3 9.96 Tf 0 -11.95 TD[(Consider)-422(the)-422(image)-422(on)-422(the)-423(righ)27(t)-421(in)-422(Figure)-422(7.7.)-711(If)-422(w)26(e)-421(cut)-422(along)]TJ/F5 9.96 Tf 287.17 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.62 TD[(ik)]TJ -0.52 -6.21 TD[(ij)]TJ/F3 9.96 Tf 13.84 2.59 TD[(=)-425(0,)-445(that)-422(is,)]TJ -306.65 -13.4 TD[(along)]TJ/F10 9.96 Tf 27.11 0 TD[(4)]TJ/F3 9.96 Tf 8.85 0 TD[(,)-401(w)27(e)-387(obtain)-387(a)-388(M\304)499(obius)-387(strip)-388(with)]TJ/F5 9.96 Tf 145.17 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.62 TD[(ik)]TJ -0.53 -6.21 TD[(ij)]TJ/F3 9.96 Tf 13.27 2.59 TD[(=)-368(0)-388(on)-388(the)-388(b)-28(oundary)83(.)-607(Cutting)-388(along)]TJ/F5 9.96 Tf -200.03 -13.4 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.62 TD[(ik)]TJ -0.52 -6.21 TD[(ij)]TJ/F3 9.96 Tf 13.25 2.59 TD[(=)]TJ/F10 9.96 Tf 11.4 0 TD[(1)]TJ/F3 9.96 Tf 9.96 0 TD[(,)-399(that)-387(is,)-400(along)]TJ/F10 9.96 Tf 69.4 0 TD[(^)]TJ/F3 9.96 Tf 6.64 0 TD[(,)-399(lea)27(v)28(es)-386(us)-387(with)-386(t)26(w)28(o)-385(pieces)-387(joined)-387(along)]TJ/F10 9.96 Tf 178.28 0 TD[(/)]TJ/F3 9.96 Tf 7.75 0 TD[(.)-604(This)-387(results)]TJ -302.32 -13.4 TD[(in)-347(a)-347(cylinder)-347(with)]TJ/F5 9.96 Tf 81.08 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.62 TD[(ik)]TJ -0.52 -6.21 TD[(ij)]TJ/F3 9.96 Tf 12.59 2.59 TD[(=)-300(0)-347(on)-347(one)-347(b)-28(oundary)-347(comp)-28(onen)27(t)-346(and)]TJ/F5 9.96 Tf 167.07 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.62 TD[(ik)]TJ -0.53 -6.21 TD[(ij)]TJ/F3 9.96 Tf 12.6 2.59 TD[(=)]TJ/F10 9.96 Tf 10.74 0 TD[(1)]TJ/F3 9.96 Tf 13.42 0 TD[(on)-346(the)-347(other)]TJ -308.77 -11.95 TD[(comp)-28(onen)27(t.)]TJ/F1 11.95 Tf 0 -30.94 TD[(7.3.5)-1125(The)-375(data)-375(map)-375(from)-375(conf)]TJ/F24 7.97 Tf 184.76 -1.79 TD[(n)]TJ/F1 11.95 Tf 10.12 1.79 TD[(to)]TJ/F22 11.95 Tf 16.43 0 TD[(AH)]TJ/F24 7.97 Tf 17.55 -1.79 TD[(n)]TJ/F1 11.95 Tf 5.63 1.79 TD[(.)]TJ/F3 9.96 Tf -234.49 -21.81 TD[(In)-400(this)-399(section)-400(w)26(e)-398(describ)-28(e)-400(a)-400(map)-400(from)-400(a)-399(set)-400(of)-400(distinct)-400(p)-28(oin)27(ts)-399(in)-400(the)-399(plane)-400(to)-400(all)]TJ 0 -11.96 TD[(angles)-292(and)-292(ho)-28(oks)-292(b)-28(et)27(w)28(een)-291(pairs)-292(and)-293(triples)-292(of)-292(those)-292(p)-28(oin)27(ts.)-430(Recall)-292(that)-292(in)-292(De\257nition)]TJ 0 -11.95 TD[(5.4)-451(w)27(e)-451(ha)27(v)28(e)-451(in)27(tro)-27(duced)-451(the)-451(reduced)-452(con\257guration)-451(space)]TJ/F4 9.96 Tf 254.12 0 TD[(conf)]TJ/F7 6.97 Tf 20.68 -1.49 TD[(n)]TJ/F3 9.96 Tf 9.92 1.49 TD[(as)-450(the)-452(space)-451(of)]TJ/F5 9.96 Tf 72.04 0 TD[(n)]TJ/F3 9.96 Tf -356.76 -11.95 TD[(distinct)-324(p)-27(oin)26(ts)-322(in)-324(the)-324(plane)-324(up)-324(to)-323(scaling)-324(and)-324(translations.)-441(F)82(or)-323(a)-323(represen)26(tativ)28(e)]TJ/F5 9.96 Tf 347.18 0 TD[(c)]TJ/F3 9.96 Tf 7.53 0 TD[(of)]TJ -354.71 -11.95 TD[(a)-291(class)-292([)]TJ/F5 9.96 Tf 33.58 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(])]TJ/F10 9.96 Tf 5.54 0 TD[(2)]TJ/F4 9.96 Tf 9.4 0 TD[(conf)]TJ/F7 6.97 Tf 20.68 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.43 1.5 TD[(,)-299(write)-291(the)-292(follo)27(wing)-290(data:)-424(for)-291(ev)27(ery)-291(pair)-291(of)-291(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 216.78 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F5 9.96 Tf 3.31 1.5 TD[(;)-167(p)]TJ/F7 6.97 Tf 9.44 -1.5 TD[(j)]TJ/F10 9.96 Tf 6.96 1.5 TD[(2)]TJ/F5 9.96 Tf 9.41 0 TD[(c;)-166(i)]TJ/F10 9.96 Tf 14.94 0 TD[(6)]TJ/F3 9.96 Tf 0 0 TD[(=)]TJ/F5 9.96 Tf 10.51 0 TD[(j)]TJ/F3 9.96 Tf 4.67 0 TD[(,)]TJ -359.97 -11.95 TD[(the)-301(undirected)-301(angle)]TJ ET 0.4 w 71.63 -257.64 m 78.04 -257.64 l S BT/F5 9.96 Tf 71.63 -263.32 TD[(\256)]TJ/F7 6.97 Tf 6.41 -1.5 TD[(ij)]TJ/F3 9.96 Tf 9.78 1.5 TD[(=)]TJ ET 0.4 w 98.33 -257.64 m 104.74 -257.64 l S BT/F5 9.96 Tf 98.33 -263.32 TD[(\256)]TJ/F7 6.97 Tf 6.41 -1.5 TD[(j)-57(i)]TJ/F3 9.96 Tf 7.01 1.5 TD[(;)-312(for)-300(ev)26(ery)-300(triple)]TJ/F5 9.96 Tf 73.05 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F5 9.96 Tf 3.32 1.5 TD[(;)-166(p)]TJ/F7 6.97 Tf 9.43 -1.5 TD[(j)]TJ/F5 9.96 Tf 4.2 1.5 TD[(;)-166(p)]TJ/F7 6.97 Tf 9.44 -1.5 TD[(k)]TJ/F3 9.96 Tf 7.89 1.5 TD[(of)-301(p)-28(oin)27(ts)-300(in)]TJ/F5 9.96 Tf 51.93 0 TD[(c)]TJ/F3 9.96 Tf 4.31 0 TD[(,)-307(the)-301(six)-301(ho)-28(oks)]TJ/F5 9.96 Tf -300.17 -13.48 TD[(h)]TJ/F7 6.97 Tf 5.74 3.62 TD[(ik)]TJ 0 -6.21 TD[(ij)]TJ/F3 9.96 Tf 9.08 2.59 TD[(,)]TJ/F5 9.96 Tf 6.26 0 TD[(h)]TJ/F7 6.97 Tf 5.73 4.79 TD[(ij)]TJ 0 -7.79 TD[(ik)]TJ/F3 9.96 Tf 9.08 3 TD[(,)]TJ/F5 9.96 Tf 6.26 0 TD[(h)]TJ/F7 6.97 Tf 5.74 4.79 TD[(j)-57(k)]TJ 0 -7.56 TD[(j)-57(i)]TJ/F3 9.96 Tf 9.96 2.77 TD[(,)]TJ/F5 9.96 Tf 6.25 0 TD[(h)]TJ/F7 6.97 Tf 5.74 4.79 TD[(j)-57(i)]TJ 0 -7.79 TD[(j)-57(k)]TJ/F3 9.96 Tf 9.96 3 TD[(,)]TJ/F5 9.96 Tf 6.26 0 TD[(h)]TJ/F7 6.97 Tf 5.73 3.62 TD[(k)-24(i)]TJ 0 -6.44 TD[(k)-24(j)]TJ/F3 9.96 Tf 9.96 2.82 TD[(,)-350(and)]TJ/F5 9.96 Tf 25.76 0 TD[(h)]TJ/F7 6.97 Tf 5.74 4.79 TD[(k)-24(j)]TJ 0 -7.79 TD[(k)-24(i)]TJ/F3 9.96 Tf 9.96 3 TD[(.)-485(This)-347(giv)27(es)]TJ/F15 9.96 Tf 55.01 8.07 TD[(\241)]TJ/F7 6.97 Tf 4.57 -3.65 TD[(n)]TJ/F12 6.97 Tf 0.47 -7.85 TD[(2)]TJ/F15 9.96 Tf 4.45 11.5 TD[(\242)]TJ/F3 9.96 Tf 8.02 -8.07 TD[(unordered)-347(angles)-346(and)-347(6)]TJ/F15 9.96 Tf 101.78 8.07 TD[(\241)]TJ/F7 6.97 Tf 4.56 -3.65 TD[(n)]TJ/F12 6.97 Tf 0.48 -7.85 TD[(3)]TJ/F15 9.96 Tf 4.45 11.5 TD[(\242)]TJ/F3 9.96 Tf 8.02 -8.07 TD[(ho)-27(oks.)]TJ -335.02 -11.95 TD[(Note)-384(that)-385(the)-384(angles)-385(and)-384(ho)-28(oks)-384(that)-385(w)27(e)-383(obtain)-385(are)-384(indep)-28(enden)27(t)-384(of)-384(the)-385(c)27(hoice)-383(of)-385(a)]TJ 0 -11.95 TD[(represen)27(tativ)28(e)-333(of)-333(a)-333(class)]TJ/F5 9.96 Tf 107.02 0 TD[(c)]TJ/F10 9.96 Tf 7.07 0 TD[(2)]TJ/F4 9.96 Tf 9.41 0 TD[(conf)]TJ/F7 6.97 Tf 20.68 -1.5 TD[(n)]TJ/F3 9.96 Tf 5.42 1.5 TD[(.)]TJ/F4 9.96 Tf -149.6 -20.92 TD[(De\257nition)-383(7.8)]TJ/F6 9.96 Tf 0 -11.95 TD[(AH)]TJ/F7 6.97 Tf 14.94 -1.49 TD[(n)]TJ/F9 9.96 Tf 8.99 1.49 TD[(is)-357(the)-358(sp)50(ac)51(e)-356(of)-358(ho)50(oks)-357(and)-358(angles)-357(on)]TJ/F5 9.96 Tf 155.51 0 TD[(n)]TJ/F9 9.96 Tf 9.55 0 TD[(p)51(oints:)]TJ/F6 9.96 Tf -132.93 -21.77 TD[(AH)]TJ/F7 6.97 Tf 14.94 -1.49 TD[(n)]TJ/F3 9.96 Tf 15.38 1.49 TD[(:=)-1000(\()]TJ/F13 9.96 Tf 24.35 0 TD[(R)]TJ/F5 9.96 Tf 7.19 0 TD[(=\274)]TJ/F13 9.96 Tf 11.02 0 TD[(Z)]TJ/F3 9.96 Tf 6.64 0 TD[(\))]TJ 3.87 3.56 TD[(\()]TJ/F14 4.98 Tf 3.87 4.03 TD[(n)]TJ/F16 4.98 Tf 0.5 -5.68 TD[(2)]TJ/F3 9.96 Tf 3.89 1.65 TD[(\))]TJ/F10 9.96 Tf 16.76 -3.56 TD[(\243)]TJ/F3 9.96 Tf 20.15 0 TD[(\()]TJ/F13 9.96 Tf 7.43 0 TD[(P)]TJ/F12 6.97 Tf 6.09 4.11 TD[(1)]TJ/F10 9.96 Tf 10.24 -4.11 TD[(\243)]TJ/F3 9.96 Tf 13.53 0 TD[(\()]TJ/F13 9.96 Tf 3.87 0 TD[(R)]TJ/F5 9.96 Tf 7.19 0 TD[(=)]TJ/F3 9.96 Tf 4.98 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(\274)]TJ/F13 9.96 Tf 6.04 0 TD[(Z)]TJ/F3 9.96 Tf 6.64 0 TD[(\))]TJ/F5 9.96 Tf 7.43 0 TD[(=)]TJ/F10 9.96 Tf 7.75 0 TD[(\273)]TJ/F7 6.97 Tf 7.75 -1.49 TD[(k)]TJ/F3 9.96 Tf 4.9 1.49 TD[(\))]TJ/F12 6.97 Tf 3.87 4.31 TD[(6)]TJ/F3 9.96 Tf 3.97 -0.75 TD[(\()]TJ/F14 4.98 Tf 3.88 4.03 TD[(n)]TJ/F16 4.98 Tf 0.49 -5.68 TD[(3)]TJ/F3 9.96 Tf 3.89 1.65 TD[(\))]TJ/F5 9.96 Tf 4.37 -3.56 TD[(;)]TJ/F9 9.96 Tf -303.91 -19.76 TD[(wher)50(e)]TJ/F10 9.96 Tf 28.13 0 TD[(\273)]TJ/F7 6.97 Tf 7.75 -1.49 TD[(k)]TJ/F9 9.96 Tf 8.46 1.49 TD[(denotes)-357(the)-358(identi\257c)50(ation)-357(de\257ne)51(d)-357(in)-358(7.1.)]TJ/F4 9.96 Tf -44.34 -20.92 TD[(Remark)-383(7.9)]TJ/F3 9.96 Tf 0 -11.95 TD[(Being)-333(a)-333(direct)-334(pro)-28(duct)-333(of)-333(circles)-334(and)-333(Klein)-333(b)-28(ottles,)]TJ/F6 9.96 Tf 224.99 0 TD[(AH)]TJ/F7 6.97 Tf 14.94 -1.49 TD[(n)]TJ/F3 9.96 Tf 8.74 1.49 TD[(is)-333(smo)-27(oth.)]TJ -248.67 -24.34 TD[(In)-228(the)-229(next)-228(de\257nition,)-250(w)27(e)-228(in)27(tro)-27(duce)-228(a)]TJ/F4 9.96 Tf 159.21 0 TD[(compacti\257cation)]TJ/F3 9.96 Tf 84.04 0 TD[(of)-228(the)-229(reduced)-228(con\257guration)]TJ -243.25 -11.96 TD[(space)]TJ/F4 9.96 Tf 26.62 0 TD[(conf)]TJ/F7 6.97 Tf 20.68 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(.)]TJ/F4 9.96 Tf -52.72 -20.91 TD[(De\257nition)-383(7.10)]TJ/F9 9.96 Tf 0 -11.95 TD[(The)]TJ/F4 9.96 Tf 20.37 0 TD[(data)-382(map)]TJ/F5 9.96 Tf 50.81 0 TD[(\303)]TJ/F6 9.96 Tf 6.48 -3.38 TD[(AH)]TJ/F14 4.98 Tf 14.94 -0.99 TD[(n)]TJ/F9 9.96 Tf 8.95 4.37 TD[(is)-357(the)-358(map)]TJ/F5 9.96 Tf -94.7 -21.54 TD[(\303)]TJ/F6 9.96 Tf 6.49 -3.38 TD[(AH)]TJ/F14 4.98 Tf 14.94 -0.99 TD[(n)]TJ/F3 9.96 Tf 8.15 4.37 TD[(:)]TJ/F4 9.96 Tf 27.34 0 TD[(conf)]TJ/F7 6.97 Tf 20.68 -1.5 TD[(n)]TJ/F10 9.96 Tf 29.99 1.5 TD[(!)]TJ/F6 9.96 Tf 19.92 0 TD[(AH)]TJ/F7 6.97 Tf 14.94 -1.5 TD[(n)]TJ/F5 9.96 Tf 5.42 1.5 TD[(;)]TJ -147.87 -15.41 TD[(\303)]TJ/F6 9.96 Tf 6.49 -3.37 TD[(AH)]TJ/F14 4.98 Tf 14.94 -1 TD[(n)]TJ/F3 9.96 Tf 8.15 4.37 TD[(:)]TJ/F4 9.96 Tf 27.34 0 TD[(conf)]TJ/F7 6.97 Tf 20.68 -1.49 TD[(n)]TJ/F10 9.96 Tf 29.99 1.49 TD[(!)]TJ/F3 9.96 Tf 19.92 0 TD[(\()]TJ/F13 9.96 Tf 3.87 0 TD[(R)]TJ/F5 9.96 Tf 7.2 0 TD[(=\274)]TJ/F13 9.96 Tf 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stream
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TD[(j)]TJ/F5 9.96 Tf 2.77 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F10 9.96 Tf 6.41 1.5 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(k)]TJ/F10 9.96 Tf 4.9 1.5 TD[(j)]TJ ET 0.4 w 143.97 -22.96 m 180.8 -22.96 l S BT 144.76 -32.28 TD[(j)]TJ/F5 9.96 Tf 2.77 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F10 9.96 Tf 5.53 1.5 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F10 9.96 Tf 4.2 1.5 TD[(j)]TJ/F3 9.96 Tf 10.84 6.83 TD[(=)]TJ/F10 9.96 Tf 15.03 6.74 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F10 9.96 Tf 5.53 1.5 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(k)]TJ/F10 9.96 Tf 4.91 1.5 TD[(j)]TJ/F3 9.96 Tf 4.98 0 TD[(+)]TJ/F10 9.96 Tf 9.96 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F10 9.96 Tf 6.41 1.5 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(k)]TJ/F10 9.96 Tf 4.9 1.5 TD[(j)]TJ ET 0.4 w 203.11 -22.96 m 288.05 -22.96 l S BT 227.96 -32.28 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.5 TD[(i)]TJ/F10 9.96 Tf 5.53 1.5 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F10 9.96 Tf 4.19 1.5 TD[(j)]TJ 34.9 6.83 TD[(\270)]TJ/F3 9.96 Tf 13.84 0 TD[(1)]TJ/F5 9.96 Tf 4.98 0 TD[(:)]TJ/F3 9.96 Tf -318.38 -35.24 TD[(\(iv\))]TJ/F5 9.96 Tf 24.07 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.78 TD[(ij)]TJ -0.53 -7.79 TD[(il)]TJ/F10 9.96 Tf 11.11 3.01 TD[(\242)]TJ/F5 9.96 Tf 4.98 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.52 -6.21 TD[(ij)]TJ/F3 9.96 Tf 15.69 2.6 TD[(=)]TJ/F10 9.96 Tf 15.03 6.73 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F10 9.96 Tf 5.53 1.49 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F10 9.96 Tf 4.2 1.49 TD[(j)]TJ ET 0.4 w 77.92 -58.2 m 113.16 -58.2 l S BT 78.49 -67.53 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F10 9.96 Tf 5.53 1.49 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(l)]TJ/F10 9.96 Tf 3.06 1.49 TD[(j)]TJ 6.75 6.84 TD[(\242)]TJ 6.17 6.73 TD[(j)]TJ/F5 9.96 Tf 2.77 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F10 9.96 Tf 5.53 1.49 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(k)]TJ/F10 9.96 Tf 4.9 1.49 TD[(j)]TJ ET 0.4 w 122.74 -58.2 m 158.69 -58.2 l S BT 123.09 -67.53 TD[(j)]TJ/F5 9.96 Tf 2.77 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F10 9.96 Tf 5.53 1.49 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F10 9.96 Tf 4.2 1.49 TD[(j)]TJ/F3 9.96 Tf 10.4 6.84 TD[(=)]TJ/F10 9.96 Tf 15.03 6.73 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F10 9.96 Tf 5.53 1.49 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(k)]TJ/F10 9.96 Tf 4.9 1.49 TD[(j)]TJ ET 0.4 w 181 -58.2 m 216.94 -58.2 l S BT 181.92 -67.53 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.49 TD[(i)]TJ/F10 9.96 Tf 5.52 1.49 TD[(\241)]TJ/F5 9.96 Tf 9.96 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.49 TD[(l)]TJ/F10 9.96 Tf 3.05 1.49 TD[(j)]TJ/F3 9.96 Tf 10.97 6.84 TD[(=)]TJ/F5 9.96 Tf 13.84 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.53 -6.44 TD[(il)]TJ/F3 9.96 Tf 9.6 2.83 TD[(.)]TJ -254.76 -18.15 TD[(\(v\))-833(Apply)-334(the)-333(de\257nition.)]TJ/F18 9.96 Tf 347.96 0 TD[(\245)]TJ/F4 9.96 Tf -354.99 -20.92 TD[(Corollary)-399(7.15)]TJ/F9 9.96 Tf 0 -11.95 TD[(F)76(or)]TJ/F5 9.96 Tf 18.59 0 TD[(x)]TJ/F10 9.96 Tf 8.46 0 TD[(2)]TJ/F5 9.96 Tf 9.41 0 TD[(X)-78(AH)]TJ/F3 9.96 Tf 25.59 0 TD[([)]TJ/F5 9.96 Tf 2.76 0 TD[(n)]TJ/F3 9.96 Tf 5.98 0 TD[(])]TJ/F9 9.96 Tf 6.33 0 TD[(and)]TJ/F5 9.96 Tf 19.35 0 TD[(i)]TJ/F9 9.96 Tf 3.43 0 TD[(,)]TJ/F5 9.96 Tf 6.62 0 TD[(j)]TJ/F9 9.96 Tf 4.67 0 TD[(,)]TJ/F5 9.96 Tf 6.61 0 TD[(k)]TJ/F9 9.96 Tf 5.5 0 TD[(,)]TJ/F5 9.96 Tf 6.62 0 TD[(l)]TJ/F9 9.96 Tf 6.73 0 TD[(distinct)-357(lab)50(els)-357(we)-358(have)]TJ -128.06 -11.95 TD[(\(i\))]TJ/F10 9.96 Tf 19.75 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.52 -6.2 TD[(ij)]TJ/F10 9.96 Tf 9.6 2.59 TD[(j)-277(2)]TJ/F3 9.96 Tf 14.94 0 TD[([0)]TJ/F5 9.96 Tf 7.75 0 TD[(;)]TJ/F10 9.96 Tf 4.42 0 TD[(1)]TJ/F3 9.96 Tf 9.96 0 TD[(])]TJ/F9 9.96 Tf 2.77 0 TD[(;)]TJ -80.64 -14.35 TD[(\(ii\))]TJ/F10 9.96 Tf 22.8 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.79 TD[(ij)]TJ -0.52 -7.79 TD[(ik)]TJ/F10 9.96 Tf 9.08 3 TD[(j)]TJ/F3 9.96 Tf 5.53 0 TD[(=)-277(1)]TJ/F5 9.96 Tf 15.49 0 TD[(=)]TJ/F10 9.96 Tf 4.98 0 TD[(j)]TJ/F5 9.96 Tf 2.77 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.62 TD[(ik)]TJ -0.53 -6.21 TD[(ij)]TJ/F10 9.96 Tf 9.61 2.59 TD[(j)]TJ/F9 9.96 Tf 2.76 0 TD[(;)]TJ -90.1 -14.57 TD[(\(iii\))]TJ/F10 9.96 Tf 25.85 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.62 TD[(ik)]TJ -0.52 -6.21 TD[(ij)]TJ/F10 9.96 Tf 9.6 2.59 TD[(j)]TJ/F3 9.96 Tf 4.98 0 TD[(+)]TJ/F10 9.96 Tf 9.96 0 TD[(j)]TJ/F5 9.96 Tf 2.77 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.79 TD[(j)-57(k)]TJ -0.53 -7.56 TD[(j)-57(i)]TJ/F10 9.96 Tf 10.49 2.77 TD[(j)-277(\270)]TJ/F3 9.96 Tf 16.04 0 TD[(1)]TJ/F9 9.96 Tf 4.98 0 TD[(;)]TJ -97.18 -14.52 TD[(\(iv\))-858(If)]TJ/F3 9.96 Tf 34.78 0 TD[(max\()]TJ/F10 9.96 Tf 25.98 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.78 TD[(ij)]TJ -0.52 -7.79 TD[(il)]TJ/F10 9.96 Tf 8.9 3.01 TD[(j)]TJ/F5 9.96 Tf 2.77 0 TD[(;)]TJ/F10 9.96 Tf 7.99 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.52 -6.21 TD[(ij)]TJ/F10 9.96 Tf 9.6 2.6 TD[(j)]TJ/F3 9.96 Tf 2.77 0 TD[(\))]TJ/F5 9.96 Tf 6.64 0 TD[(<)]TJ/F10 9.96 Tf 10.51 0 TD[(1)]TJ/F9 9.96 Tf 9.96 0 TD[(,)-357(then)]TJ/F10 9.96 Tf 28.76 0 TD[(j)]TJ/F5 9.96 Tf 2.77 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.78 TD[(ij)]TJ -0.53 -7.79 TD[(il)]TJ/F10 9.96 Tf 8.9 3.01 TD[(j)-222(\242)-222(j)]TJ/F5 9.96 Tf 12.73 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.53 -6.21 TD[(ij)]TJ/F10 9.96 Tf 9.61 2.6 TD[(j)]TJ/F3 9.96 Tf 5.53 0 TD[(=)]TJ/F10 9.96 Tf 10.51 0 TD[(j)]TJ/F5 9.96 Tf 2.77 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.53 -6.44 TD[(il)]TJ/F10 9.96 Tf 9.61 2.83 TD[(j)]TJ/F9 9.96 Tf 2.76 0 TD[(.)]TJ/F4 9.96 Tf -251.55 -24.75 TD[(Pro)-31(of.)]TJ/F3 9.96 Tf 35.98 0 TD[(The)-421(claims)-422(follo)27(w)-421(from)-421(Lemma)-422(7.14)-422(b)27(y)-420(taking)-422(limits,)-444(but)-421(notice)-422(that)-422(for)]TJ/F5 9.96 Tf -35.98 -11.95 TD[(x)]TJ/F10 9.96 Tf 8.46 0 TD[(2)]TJ/F6 9.96 Tf 9.4 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.5 TD[(n)]TJ/F3 9.96 Tf 8.75 1.5 TD[(some)]TJ/F5 9.96 Tf 24.95 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 3.61 TD[(ik)]TJ -0.53 -6.2 TD[(ij)]TJ/F3 9.96 Tf 12.93 2.59 TD[(can)-333(b)-27(e)-334(negativ)27(e,)-332(see)-334(De\257nition)-333(7.8.)]TJ/F18 9.96 Tf 262.46 0 TD[(\245)]TJ/F1 11.95 Tf -354.99 -32.17 TD[(7.4.3)-1124(Separating)-375(clusters.)]TJ/F4 9.96 Tf 0 -21.99 TD[(Remark)-383(7.16)]TJ/F3 9.96 Tf 0 -11.95 TD[(F)83(or)-332(the)-334(rest)-333(of)-333(this)-334(section,)-333(w)27(e)-333(iden)27(tify)-332(a)-333(site)]TJ/F5 9.96 Tf 198.78 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 6.64 1.49 TD[(with)-333(its)-333(lab)-28(el)]TJ/F5 9.96 Tf 60.64 0 TD[(i)]TJ/F3 9.96 Tf 3.43 0 TD[(.)]TJ -274.5 -24.34 TD[(Set)]TJ/F5 9.96 Tf 110.9 -12.55 TD[(C)]TJ/F7 6.97 Tf 7.12 -1.5 TD[(ij)]TJ/F3 9.96 Tf 13.1 1.5 TD[(:=)]TJ/F10 9.96 Tf 16.6 0 TD[(f)]TJ/F5 9.96 Tf 4.98 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(k)]TJ/F10 9.96 Tf 8.22 1.5 TD[(j)-333(j)]TJ/F5 9.96 Tf 8.86 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.78 TD[(ij)]TJ -0.53 -7.79 TD[(ik)]TJ/F10 9.96 Tf 9.08 3.01 TD[(j)]TJ/F5 9.96 Tf 5.53 0 TD[(>)]TJ/F3 9.96 Tf 10.52 0 TD[(0)]TJ/F10 9.96 Tf 4.98 0 TD[(g)-221([)-222(f)]TJ/F5 9.96 Tf 21.02 0 TD[(i;)-166(j)]TJ/F10 9.96 Tf 12.53 0 TD[(g)]TJ/F5 9.96 Tf 4.98 0 TD[(:)]TJ/F3 9.96 Tf 93.2 0 TD[(\(7.2\))]TJ -342.26 -23.41 TD[(In)27(tuitiv)28(ely)84(,)-310(think)-306(of)-305(the)-305(follo)27(wing.)-434(Recall)-306(the)-305(geometric)-305(in)27(terpretation)-305(of)-305(a)-305(ho)-28(ok)]TJ/F5 9.96 Tf 347.92 0 TD[(h)]TJ/F7 6.97 Tf 5.73 4.79 TD[(ij)]TJ 0 -7.79 TD[(ik)]TJ/F3 9.96 Tf -353.65 -8.95 TD[(giv)27(en)-282(in)-283(Section)-283(7.3.2.)-427(Supp)-28(ose)-283(w)27(e)-282(use)]TJ/F5 9.96 Tf 167.91 0 TD[(h)]TJ/F7 6.97 Tf 5.74 3.61 TD[(ik)]TJ 0 -6.2 TD[(ij)]TJ/F3 9.96 Tf 11.9 2.59 TD[(to)-282(dra)27(w)-282(a)-283(p)-28(oin)27(t)]TJ/F5 9.96 Tf 69.12 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 7.02 1.49 TD[(in)-282(the)-283(plane,)-293(giv)26(en)-282(the)]TJ -266.7 -14.34 TD[(p)-27(oin)27(ts)]TJ/F5 9.96 Tf 30.4 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F3 9.96 Tf 7.11 1.5 TD[(and)]TJ/F5 9.96 Tf 19.83 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(k)]TJ/F3 9.96 Tf 4.9 1.5 TD[(.)-585(The)-380(ratio)]TJ/F10 9.96 Tf 53.83 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.78 TD[(ij)]TJ -0.52 -7.79 TD[(ik)]TJ/F10 9.96 Tf 9.07 3.01 TD[(j)]TJ/F3 9.96 Tf 6.56 0 TD[(giv)27(es)-379(the)-380(distance)-380(b)-28(et)27(w)27(een)-379(the)-380(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 168.69 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F3 9.96 Tf 7.1 1.5 TD[(and)]TJ/F5 9.96 Tf 19.84 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(,)]TJ -359.97 -13.4 TD[(compared)-288(to)-289(the)-289(unit)-288(distance)]TJ/F5 9.96 Tf 132.32 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F5 9.96 Tf 3.32 1.5 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(k)]TJ/F3 9.96 Tf 4.9 1.5 TD[(.)-429(Imagine)-289(an)-288(observ)26(er)-287(situated)-289(at)]TJ/F5 9.96 Tf 146.36 0 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.5 TD[(k)]TJ/F3 9.96 Tf 4.9 1.5 TD[(.)-429(When)]TJ/F10 9.96 Tf 35.65 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.78 TD[(ij)]TJ -0.52 -7.79 TD[(ik)]TJ/F10 9.96 Tf 9.08 3.01 TD[(j)]TJ/F3 9.96 Tf -359.97 -13.4 TD[(gets)-333(v)27(ery)-333(small,)]TJ/F5 9.96 Tf 71.25 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 7.52 1.5 TD[(mo)27(v)28(es)-333(v)27(ery)-332(close)-334(to)]TJ/F5 9.96 Tf 87.58 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F3 9.96 Tf 3.31 1.5 TD[(.)-445(But)-334(as)-334(long)-333(as)]TJ/F10 9.96 Tf 73.04 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(\257)]TJ/F7 6.97 Tf 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TD[(L)]TJ/F7 6.97 Tf 6.78 -1.5 TD[(x)]TJ/F3 9.96 Tf 5.02 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\))-475(equals)-476(\()]TJ/F5 9.96 Tf 44.12 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(p)]TJ/F12 6.97 Tf 9.44 -1.5 TD[(3)]TJ/F5 9.96 Tf 4.46 1.5 TD[(;)-167(p)]TJ/F12 6.97 Tf 9.44 -1.5 TD[(1)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\).)-872(In)-476(b)-28(oth)-476(screens)]TJ/F5 9.96 Tf 89.45 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 9.6 1.5 TD[(=)-516(\(0)]TJ/F5 9.96 Tf 21.74 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\).)-872(In)-476(the)-476(top)-476(screen,)]TJ/F5 9.96 Tf -261.45 -11.95 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(3)]TJ/F3 9.96 Tf 7.24 1.5 TD[(=)-277(\(cos)]TJ/F10 9.96 Tf 29.38 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.5 TD[(S)]TJ/F16 4.98 Tf 4.89 -1.33 TD[([6])]TJ/F5 9.96 Tf 8.4 2.83 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(sin)]TJ/F10 9.96 Tf 13.89 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.5 TD[(S)]TJ/F16 4.98 Tf 4.89 -1.33 TD[([6])]TJ/F3 9.96 Tf 8.4 2.83 TD[(\),)-304(where)]TJ/F10 9.96 Tf 38.12 0 TD[(O)]TJ/F7 6.97 Tf 7.92 -1.5 TD[(S)]TJ/F16 4.98 Tf 4.9 -1.33 TD[([6])]TJ/F3 9.96 Tf 11.16 2.83 TD[(=)]TJ/F5 9.96 Tf 10.51 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(13)]TJ/F3 9.96 Tf 8.44 1.5 TD[(.)-432(W)82(e)-296(determine)-298(the)-297(p)-28(osition)-297(of)]TJ/F5 9.96 Tf 135.4 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 7.43 1.5 TD[(in)-297(the)]TJ -337.64 -11.96 TD[(top)-333(screen,)-333(using)-334(Equation)-333(7.4:)]TJ/F5 9.96 Tf 41.09 -19.77 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F12 6.97 Tf 6.11 -1.8 TD[([6])]TJ/F3 9.96 Tf 8.97 1.8 TD[(\))-611(=)]TJ/F5 9.96 Tf 23.8 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 4.11 TD[(12)]TJ -0.53 -6.57 TD[(13)]TJ/F4 9.96 Tf 10.33 2.46 TD[(rot)]TJ/F7 6.97 Tf 14.89 -2.18 TD[(\256)]TJ/F16 4.98 Tf 5.18 2.4 TD[(12)]TJ 0 -4.56 TD[(13)]TJ/F3 9.96 Tf 9 4.34 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(3)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\))-611(=)]TJ/F5 9.96 Tf 23.79 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 4.11 TD[(12)]TJ -0.52 -6.57 TD[(13)]TJ/F3 9.96 Tf 10.32 2.46 TD[(\(cos)]TJ/F5 9.96 Tf 18.87 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(13)]TJ/F3 9.96 Tf 10.65 1.5 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.41 4.11 TD[(12)]TJ -0.04 -6.57 TD[(13)]TJ/F5 9.96 Tf 9.84 2.46 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(sin)]TJ/F5 9.96 Tf 13.88 0 TD[(\256)]TJ/F12 6.97 Tf 6.38 -1.5 TD[(13)]TJ/F3 9.96 Tf 10.65 1.5 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.4 4.11 TD[(12)]TJ -0.03 -6.57 TD[(13)]TJ/F3 9.96 Tf 9.83 2.46 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(:)]TJ/F3 9.96 Tf -318.89 -19.78 TD[(In)]TJ/F5 9.96 Tf 12.45 0 TD[(S)]TJ/F12 6.97 Tf 6.11 -1.49 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.37 0 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.36 0 TD[(6)]TJ/F3 9.96 Tf 4.47 1.49 TD[(,)-333(ho)27(w)28(ev)28(er,)]TJ/F5 9.96 Tf 47.06 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 7.79 1.49 TD[(is)-333(the)-333(\257rst)-333(site)-334(in)-333(the)-333(second)-334(cluster,)-333(so)]TJ/F5 9.96 Tf 1.28 -19.78 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F12 6.97 Tf 6.11 -1.49 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.37 0 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.36 0 TD[(6)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\))-999(=)-1000(\(cos)]TJ/F10 9.96 Tf 50.41 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(S)]TJ/F16 4.98 Tf 4.89 -1 TD[(1)]TJ/F14 4.98 Tf 3.39 0 TD[(;)]TJ/F16 4.98 Tf 2.28 0 TD[(2)]TJ/F14 4.98 Tf 3.39 0 TD[(;)]TJ/F16 4.98 Tf 2.28 0 TD[(6)]TJ/F5 9.96 Tf 4.39 2.49 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(sin)]TJ/F10 9.96 Tf 13.89 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(S)]TJ/F16 4.98 Tf 4.89 -1 TD[(1)]TJ/F14 4.98 Tf 3.39 0 TD[(;)]TJ/F16 4.98 Tf 2.28 0 TD[(2)]TJ/F14 4.98 Tf 3.39 0 TD[(;)]TJ/F16 4.98 Tf 2.28 0 TD[(6)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(:)]TJ/F3 9.96 Tf -263.13 -19.77 TD[(According)-333(to)-333(Step)-334(2)-333(in)-333(Construction)-334(7.42,)]TJ/F10 9.96 Tf 99.4 -19.78 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(S)]TJ/F16 4.98 Tf 4.89 -1 TD[(1)]TJ/F14 4.98 Tf 3.39 0 TD[(;)]TJ/F16 4.98 Tf 2.28 0 TD[(2)]TJ/F14 4.98 Tf 3.39 0 TD[(;)]TJ/F16 4.98 Tf 2.28 0 TD[(6)]TJ/F3 9.96 Tf 10.47 2.49 TD[(=)]TJ/F10 9.96 Tf 13.84 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(S)]TJ/F16 4.98 Tf 4.89 -1.34 TD[([6])]TJ/F3 9.96 Tf 10.61 2.83 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.41 4.11 TD[(12)]TJ -0.04 -6.57 TD[(13)]TJ/F3 9.96 Tf 15.92 2.46 TD[(=)]TJ/F5 9.96 Tf 13.83 0 TD[(\256)]TJ/F12 6.97 Tf 6.38 -1.49 TD[(13)]TJ/F3 9.96 Tf 10.65 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.41 4.11 TD[(12)]TJ -0.04 -6.57 TD[(13)]TJ/F3 9.96 Tf 9.83 2.46 TD[(,)]TJ -260.57 -19.78 TD[(as)]TJ/F5 9.96 Tf 12.45 0 TD[(i)]TJ/F12 6.97 Tf 3.43 -1.49 TD[(1)]TJ/F3 9.96 Tf 7.59 1.49 TD[(=)-314(1,)]TJ/F5 9.96 Tf 22.21 0 TD[(i)]TJ/F12 6.97 Tf 3.43 -1.49 TD[(2)]TJ/F3 9.96 Tf 7.6 1.49 TD[(=)-313(3)-355(and)]TJ/F5 9.96 Tf 38.97 0 TD[(j)]TJ/F12 6.97 Tf 4.1 -1.49 TD[(1)]TJ/F3 9.96 Tf 7.6 1.49 TD[(=)-313(1)]TJ/F5 9.96 Tf 15.85 0 TD[(;)-166(j)]TJ/F12 6.97 Tf 8.53 -1.49 TD[(2)]TJ/F3 9.96 Tf 7.59 1.49 TD[(=)-314(2.)-509(W)82(e)-354(conclude)-355(that)-355(the)-355(only)-355(di\256erence)-355(b)-28(et)27(w)28(een)]TJ -139.35 -11.95 TD[(the)-420(argumen)26(t)-419(of)]TJ/F5 9.96 Tf 75.68 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(3)]TJ/F3 9.96 Tf 8.66 1.49 TD[(in)]TJ/F5 9.96 Tf 12.49 0 TD[(S)]TJ/F12 6.97 Tf 6.11 -1.8 TD[([6])]TJ/F3 9.96 Tf 13.16 1.8 TD[(and)]TJ/F5 9.96 Tf 20.24 0 TD[(S)]TJ/F12 6.97 Tf 6.11 -1.49 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.36 0 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.37 0 TD[(6)]TJ/F3 9.96 Tf 8.66 1.49 TD[(can)-420(b)-28(e)-420(caused)-421(b)27(y)]TJ/F5 9.96 Tf 81.28 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.62 TD[(12)]TJ -0.53 -6.09 TD[(13)]TJ/F3 9.96 Tf 10.32 2.47 TD[(:)-619(this)-421(ratio)-420(is)-421(used)-421(in)]TJ -266.02 -11.95 TD[(dra)27(wing)]TJ/F5 9.96 Tf 38.51 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 8.37 1.49 TD[(in)]TJ/F5 9.96 Tf 12.19 0 TD[(S)]TJ/F12 6.97 Tf 6.11 -1.8 TD[([6])]TJ/F3 9.96 Tf 12.88 1.8 TD[(but)-390(not)-392(used)-391(in)-391(dra)27(wing)]TJ/F5 9.96 Tf 111.14 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.49 TD[(2)]TJ/F3 9.96 Tf 8.36 1.49 TD[(in)]TJ/F5 9.96 Tf 12.2 0 TD[(S)]TJ/F12 6.97 Tf 6.11 -1.49 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.36 0 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.37 0 TD[(6)]TJ/F3 9.96 Tf 4.47 1.49 TD[(.)-617(Indeed,)-406(sign\()]TJ/F5 9.96 Tf 67.52 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.61 TD[(12)]TJ -0.53 -6.08 TD[(13)]TJ/F3 9.96 Tf 11.99 2.47 TD[(\))-374(=)]TJ/F10 9.96 Tf 19.07 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(1,)]TJ -354.99 -11.95 TD[(whic)27(h)-332(causes)-334(a)]TJ/F5 9.96 Tf 67.34 0 TD[(\274)]TJ/F3 9.96 Tf 9.36 0 TD[(shift)-333(in)-333(arg\()]TJ/F5 9.96 Tf 51.82 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\))-332(from)-334(the)-333(top)-333(screen)-334(to)-333(the)-333(screen)]TJ/F5 9.96 Tf 154.84 0 TD[(S)]TJ/F12 6.97 Tf 6.11 -1.5 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.37 0 TD[(2)]TJ/F7 6.97 Tf 3.97 0 TD[(;)]TJ/F12 6.97 Tf 2.36 0 TD[(6)]TJ/F3 9.96 Tf 4.47 1.5 TD[(.)]TJ/F1 14.34 Tf -316.09 -36 TD[(7.7)-1125(Reading)-375(o\256)-375(data)-375(elemen)31(ts)-374(from)-375(\257lled)-375(screens.)]TJ/F3 9.96 Tf 0 -25.25 TD[(Let)]TJ/F5 9.96 Tf 18.61 0 TD[(q)]TJ/F10 9.96 Tf 8.84 0 TD[(2)]TJ/F4 9.96 Tf 10.68 0 TD[(Dom)]TJ/F7 6.97 Tf 24.06 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(\).)-674(Supp)-27(ose)-410(w)26(e)-409(ha)27(v)28(e)-409(\257lled)-410(the)]TJ/F5 9.96 Tf 135.36 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(-screens)-409(with)]TJ/F5 9.96 Tf 61.42 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(-sites)-410(b)27(y)-409(applying)]TJ/F4 9.96 Tf -284.46 -11.95 TD[(dra)31(w)]TJ/F7 6.97 Tf 24.61 -1.49 TD[(x)]TJ/F3 9.96 Tf 5.01 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\).)-697(In)-418(this)-418(section)-418(w)27(e)-417(tell)-418(exactly)-418(ho)27(w)-417(to)-418(read)-417(o\256)-418(angles)-418(and)-418(ho)-28(oks)-418(co)-27(or-)]TJ -38.3 -11.95 TD[(dinates)-444(from)-444(the)]TJ/F5 9.96 Tf 78.37 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(-\257lled)]TJ/F5 9.96 Tf 28.77 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-screens.)-776(More)-445(precisely)83(,)-471(w)27(e)-443(explain)-445(ho)27(w)-443(to)-444(determine)]TJ -117.64 -11.95 TD[(ev)27(ery)-309(angle)]TJ ET 0.4 w 32.02 -350.9 m 45.41 -350.9 l S BT/F5 9.96 Tf 32.02 -356.58 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.5 TD[(ij)]TJ/F3 9.96 Tf 10.11 1.5 TD[(b)-27(et)27(w)28(een)-310(t)27(w)28(o)-309(sites)]TJ/F5 9.96 Tf 78.82 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F3 9.96 Tf 3.32 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-310(and)]TJ/F5 9.96 Tf 26.1 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F3 9.96 Tf 4.2 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))-309(and)-311(ev)27(ery)-309(ho)-28(ok)]TJ/F5 9.96 Tf 76.29 0 TD[(h)]TJ/F7 6.97 Tf 5.74 4.78 TD[(ij)]TJ 0 -7.79 TD[(ik)]TJ/F3 9.96 Tf 12.17 3.01 TD[(b)-27(et)26(w)28(een)-309(three)]TJ -302.35 -11.96 TD[(sites)]TJ/F5 9.96 Tf 22.45 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.31 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\),)]TJ/F5 9.96 Tf 10.21 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F3 9.96 Tf 4.19 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\),)-358(and)]TJ/F5 9.96 Tf 29.77 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(k)]TJ/F3 9.96 Tf 4.91 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\).)-504(Basically)-353(w)27(e)-353(read)-353(o\256)-353(lac)27(king)-353(co)-27(ordinates)-354(in)-353(a)-353(suitable)]TJ/F5 9.96 Tf -115.9 -11.95 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(-screen.)-442(Recall)-327(the)-328(notions)-327(of)-327(separating)-328(clusters)-327(and)-328(separating)-327(screens)-328(that)-327(w)26(ere)]TJ -5.7 -11.95 TD[(in)27(tro)-27(duced)-368(in)-368(De\257nition)-368(7.24.)-548(These)-368(notions)-368(are)-367(used)-368(for)-368(\257xing)-368(the)]TJ/F5 9.96 Tf 300.07 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-screens)-367(used)]TJ -305.76 -11.95 TD[(for)-333(determining)-333(the)-334(angles)-333(and)-333(ho)-28(oks)-334(co)-27(ordinates.)]TJ/F4 9.96 Tf 0 -20.92 TD[(Remark)-383(7.48)]TJ/F3 9.96 Tf 0 -11.95 TD[(The)-462(separating)-461(screen)]TJ/F5 9.96 Tf 102.5 0 TD[(S)]TJ/F7 6.97 Tf 6.11 -1.49 TD[(ij)]TJ/F3 9.96 Tf 7.01 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))-461(is)-462(the)-462(only)]TJ/F5 9.96 Tf 61.33 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(-screen)-461(in)-462(whic)27(h)-461(it)-462(is)-461(guaran)26(teed)-460(that)]TJ/F5 9.96 Tf -192.22 -11.95 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.32 1.49 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TD[(t)]TJ/F3 9.96 Tf 3.5 1.49 TD[(.)-747(W)82(e)-433(use)]TJ -320.48 -11.95 TD[(Equation)-333(7.5)-333(for)-334(determining)]TJ/F5 9.96 Tf 129.68 0 TD[(\257)]TJ/F7 6.97 Tf 6.15 4.78 TD[(j)]TJ/F16 4.98 Tf 3.3 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.89 0.99 TD[(j)]TJ/F14 4.98 Tf 3.29 -0.99 TD[(t)]TJ/F7 6.97 Tf -11 -6.57 TD[(j)]TJ/F16 4.98 Tf 3.29 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.89 0.99 TD[(j)]TJ/F16 4.98 Tf 3.3 -0.99 TD[(2)]TJ/F3 9.96 Tf 5.74 3.77 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\),)-333(while)-333(remem)27(b)-27(ering)-334(that)]TJ/F5 9.96 Tf 117.36 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(1)]TJ/F3 9.96 Tf 7.24 1.5 TD[(=)-277(\(0)]TJ/F5 9.96 Tf 19.36 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\).)]TJ/F5 9.96 Tf -175.72 -27.58 TD[(\257)]TJ/F12 6.97 Tf 6.16 4.11 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.49 -6.58 TD[(12)]TJ/F3 9.96 Tf 9.79 2.47 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-1000(=)]TJ/F5 9.96 Tf 33.22 6.73 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(t)]TJ/F10 9.96 Tf 5.72 1.49 TD[(\242)]TJ/F5 9.96 Tf 4.98 0 TD[(p)]TJ/F17 6.97 Tf 5.01 3.62 TD[(0)]TJ/F12 6.97 Tf 0 -6.09 TD[(2)]TJ ET 0.4 w 174.9 -46.39 m 201.05 -46.39 l S BT/F5 9.96 Tf 174.9 -55.72 TD[(p)]TJ/F17 6.97 Tf 5.01 3.44 TD[(0)]TJ/F12 6.97 Tf 0 -6.09 TD[(2)]TJ/F10 9.96 Tf 6.68 2.65 TD[(\242)]TJ/F5 9.96 Tf 4.98 0 TD[(p)]TJ/F17 6.97 Tf 5.01 3.44 TD[(0)]TJ/F12 6.97 Tf 0 -6.09 TD[(2)]TJ/F5 9.96 Tf 5.66 9.49 TD[(:)]TJ/F3 9.96 Tf 120.18 0 TD[(\(7.7\))]TJ/F5 9.96 Tf -342.26 -26.2 TD[(p)]TJ/F17 6.97 Tf 5.01 3.61 TD[(0)]TJ/F12 6.97 Tf 0 -6.08 TD[(2)]TJ/F3 9.96 Tf 7.79 2.47 TD[(is)-333(giv)27(en)-333(b)27(y)]TJ/F5 9.96 Tf 44.26 -20.18 TD[(p)]TJ/F17 6.97 Tf 5.01 4.11 TD[(0)]TJ/F12 6.97 Tf 0 -6.57 TD[(2)]TJ/F3 9.96 Tf 10.55 2.46 TD[(=)]TJ/F4 9.96 Tf 13.84 0 TD[(rot)]TJ/F7 6.97 Tf 14.89 -2.18 TD[(\256)]TJ/F16 4.98 Tf 5.18 2.4 TD[(1)]TJ/F14 4.98 Tf 3.39 0 TD[(t)]TJ/F16 4.98 Tf -3.39 -4.56 TD[(12)]TJ/F5 9.96 Tf 9 4.34 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 10.55 1.5 TD[(=)-611(\(cos[)]TJ/F10 9.96 Tf 33.81 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.5 TD[(S)]TJ/F3 9.96 Tf 7.99 1.5 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.4 4.11 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4 -6.57 TD[(12)]TJ/F3 9.96 Tf 9.8 2.46 TD[(\()-73(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\)])]TJ/F5 9.96 Tf 6.64 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(sin[)]TJ/F10 9.96 Tf 14.99 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.5 TD[(S)]TJ/F3 9.96 Tf 7.99 1.5 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F12 6.97 Tf 6.4 4.11 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4 -6.57 TD[(12)]TJ/F3 9.96 Tf 9.8 2.46 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\)]\))]TJ/F5 9.96 Tf 10.52 0 TD[(:)]TJ/F3 9.96 Tf -302.92 -21.67 TD[(Therefore)]TJ/F10 9.96 Tf 46.76 0 TD[(j)]TJ/F5 9.96 Tf 2.76 0 TD[(p)]TJ/F17 6.97 Tf 5.02 3.61 TD[(0)]TJ/F12 6.97 Tf 0 -6.09 TD[(2)]TJ/F10 9.96 Tf 4.46 2.48 TD[(j)]TJ/F3 9.96 Tf 8.21 0 TD[(=)-546(1,)-534(so)]TJ/F5 9.96 Tf 40.09 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.61 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.5 -6.09 TD[(12)]TJ/F3 9.96 Tf 9.8 2.48 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))-494(reduces)-494(to)]TJ/F5 9.96 Tf 59.67 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.61 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.49 -6.09 TD[(12)]TJ/F3 9.96 Tf 9.79 2.48 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-546(=)]TJ/F5 9.96 Tf 22.5 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(t)]TJ/F10 9.96 Tf 6.79 1.5 TD[(\242)]TJ/F5 9.96 Tf 6.05 0 TD[(p)]TJ/F17 6.97 Tf 5.01 3.61 TD[(0)]TJ/F12 6.97 Tf 0 -6.09 TD[(2)]TJ/F3 9.96 Tf 4.47 2.48 TD[(.)-927(Observ)27(e)-493(that)]TJ/F5 9.96 Tf 75.05 0 TD[(p)]TJ/F12 6.97 Tf 5.01 -1.5 TD[(2)]TJ/F3 9.96 Tf 9.91 1.5 TD[(=)]TJ -354.99 -11.96 TD[(\(cos)]TJ/F10 9.96 Tf 18.87 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(S)]TJ/F5 9.96 Tf 5.77 1.49 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(sin)]TJ/F10 9.96 Tf 13.89 0 TD[(O)]TJ/F7 6.97 Tf 7.92 -1.49 TD[(S)]TJ/F3 9.96 Tf 5.77 1.49 TD[(\))-382(and)-382(apply)-382(Lemma)-382(7.53.)-591(If)]TJ/F5 9.96 Tf 128.25 0 TD[(\257)]TJ/F12 6.97 Tf 6.15 3.62 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.49 -6.09 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf 7.45 0 TD[(>)]TJ/F3 9.96 Tf 11.32 0 TD[(0,)-394(then)]TJ/F5 9.96 Tf 34.85 0 TD[(\256)]TJ/F12 6.97 Tf 6.41 3.62 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.01 -6.09 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))-358(=)]TJ/F5 9.96 Tf 18.77 0 TD[(\256)]TJ/F12 6.97 Tf 6.4 3.62 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4 -6.09 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-382(and)]TJ -339.01 -11.95 TD[(b)27(y)-373(ev)54(aluating)-373(Equation)-375(7.7)-374(it)-375(follo)27(ws)-373(that)]TJ/F5 9.96 Tf 187.87 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.62 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.49 -6.09 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-346(=)]TJ/F5 9.96 Tf 18.52 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.62 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.5 -6.09 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\).)-567(If,)-385(on)-374(the)-375(other)-374(hand,)]TJ/F5 9.96 Tf -254.61 -11.95 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.61 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.49 -6.08 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf 8.98 0 TD[(<)]TJ/F3 9.96 Tf 12.86 0 TD[(0,)-509(then)]TJ/F5 9.96 Tf 36.91 0 TD[(\256)]TJ/F12 6.97 Tf 6.41 3.61 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4 -6.08 TD[(12)]TJ/F3 9.96 Tf 9.79 2.47 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-513(=)]TJ/F5 9.96 Tf 21.84 0 TD[(\256)]TJ/F12 6.97 Tf 6.41 3.61 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.01 -6.08 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))-315(+)]TJ/F5 9.96 Tf 17.92 0 TD[(\274)]TJ/F3 9.96 Tf 6.03 0 TD[(,)-509(so)]TJ/F5 9.96 Tf 21.48 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(t)]TJ/F3 9.96 Tf 8.61 1.49 TD[(=)]TJ/F10 9.96 Tf 12.86 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.61 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.5 -6.08 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(p)]TJ/F17 6.97 Tf 5.01 3.61 TD[(0)]TJ/F12 6.97 Tf 0 -6.08 TD[(2)]TJ/F3 9.96 Tf 4.47 2.47 TD[(,)-509(whic)27(h)-474(implies)-474(that)]TJ/F5 9.96 Tf -271.52 -11.95 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.61 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.49 -6.08 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(\()-73(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-277(=)]TJ/F10 9.96 Tf 17.15 0 TD[(\241)]TJ/F5 9.96 Tf 7.75 0 TD[(\257)]TJ/F12 6.97 Tf 6.16 3.61 TD[(1)]TJ/F7 6.97 Tf 3.97 0 TD[(t)]TJ/F12 6.97 Tf -4.49 -6.08 TD[(12)]TJ/F3 9.96 Tf 9.79 2.47 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\),)-333(as)-333(claimed.)]TJ/F18 9.96 Tf 281.87 0 TD[(\245)]TJ/F4 9.96 Tf -354.99 -20.92 TD[(Example)-383(7.55)]TJ/F3 9.96 Tf 0 -11.95 TD[(In)-340(the)-341(ho)-28(ok)27(ed)-339(tree)-341(in)-341(our)-340(running)-341(example,)-342(see)-341(Examples)-340(7.13,)-343(7.32,)-342(7.38,)-342(7.47)-341(and)]TJ 0 -11.95 TD[(7.52,)-407(t)26(w)28(o)]TJ/F5 9.96 Tf 43.94 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-t)27(yp)-27(e)-393(3)-392(ho)-28(oks)-393(o)-28(ccur,)]TJ/F5 9.96 Tf 94.46 0 TD[(h)]TJ/F12 6.97 Tf 5.73 3.61 TD[(14)]TJ 0 -6.08 TD[(13)]TJ/F3 9.96 Tf 13.71 2.47 TD[(and)]TJ/F5 9.96 Tf 19.96 0 TD[(h)]TJ/F12 6.97 Tf 5.74 3.61 TD[(16)]TJ 0 -6.08 TD[(12)]TJ/F3 9.96 Tf 9.8 2.47 TD[(.)-622(The)]TJ/F5 9.96 Tf 30.03 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(-v)55(alues,)-406(that)-393(are)-393(those)-393(v)55(alues)]TJ -233.87 -11.95 TD[(that)-289(where)-290(used)-289(to)]TJ/F9 9.96 Tf 83.55 0 TD[(\257l)-51(l)]TJ/F3 9.96 Tf 14.08 0 TD[(the)]TJ/F5 9.96 Tf 16.72 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(-screens,)-298(and)-290(the)]TJ/F4 9.96 Tf 75.28 0 TD[(read)]TJ/F7 6.97 Tf 21.9 -1.5 TD[(x)]TJ/F3 9.96 Tf 5.01 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\)-v)55(alues,)-297(the)-289(v)54(alues)-288(that)-290(where)]TJ/F9 9.96 Tf -230.91 -11.95 TD[(r)50(e)51(ad)-356(o\256)]TJ/F3 9.96 Tf 36.03 0 TD[(from)-333(the)-333(\257lled)]TJ/F5 9.96 Tf 65.04 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(-screens,)-332(are)-334(collected)-333(in)-333(T)82(able)-332(7.4.)]TJ/F5 9.96 Tf 11.24 -30.53 TD[(q)]TJ/F3 9.96 Tf 8.12 0 TD[(co)-27(ordinate)]TJ/F4 9.96 Tf 59.86 0 TD[(read)]TJ/F7 6.97 Tf 21.89 -1.49 TD[(x)]TJ/F3 9.96 Tf 5.02 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))-332(co)-28(ordinate)]TJ/F5 9.96 Tf -133.29 -23.9 TD[(h)]TJ/F12 6.97 Tf 5.74 3.61 TD[(14)]TJ 0 -6.09 TD[(13)]TJ/F3 9.96 Tf 21.75 2.48 TD[(\()]TJ/F10 9.96 Tf 9.41 0 TD[(\241)]TJ/F3 9.96 Tf 9.96 0 TD[(1)]TJ/F5 9.96 Tf 4.98 0 TD[(:)]TJ/F3 9.96 Tf 2.77 0 TD[(92)]TJ/F5 9.96 Tf 9.96 0 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(4)]TJ/F17 6.97 Tf 4.98 3.61 TD[(\261)]TJ/F3 9.96 Tf 7.9 -3.61 TD[(\))-2438(\()-334(1)]TJ/F5 9.96 Tf 40.34 0 TD[(:)]TJ/F3 9.96 Tf 2.76 0 TD[(92)]TJ/F5 9.96 Tf 9.96 0 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(176)]TJ/F17 6.97 Tf 14.94 3.61 TD[(\261)]TJ/F3 9.96 Tf 7.9 -3.61 TD[(\))]TJ/F5 9.96 Tf -169.95 -11.96 TD[(h)]TJ/F12 6.97 Tf 5.74 3.62 TD[(16)]TJ 0 -6.09 TD[(12)]TJ/F3 9.96 Tf 23.97 2.47 TD[(\()]TJ/F5 9.96 Tf 7.19 0 TD[(:)]TJ/F3 9.96 Tf 2.77 0 TD[(91)]TJ/F5 9.96 Tf 9.96 0 TD[(;)]TJ/F10 9.96 Tf 4.42 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(11)]TJ/F17 6.97 Tf 9.96 3.62 TD[(\261)]TJ/F3 9.96 Tf 7.9 -3.62 TD[(\))-3160(\()]TJ/F5 9.96 Tf 42.55 0 TD[(:)]TJ/F3 9.96 Tf 2.76 0 TD[(91)]TJ/F5 9.96 Tf 9.96 0 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(11)]TJ/F17 6.97 Tf 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Tf -10.53 -6.57 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.88 0.99 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(2)]TJ/F3 9.96 Tf 6.75 3.77 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\).)-646(F)83(or)-400(this)-401(purp)-27(ose)-401(w)27(e)-400(compute)-400(the)-401(co)-28(ordinates)-400(of)]TJ/F5 9.96 Tf 229.64 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F3 9.96 Tf 4.39 2.49 TD[(,)]TJ/F5 9.96 Tf -359.97 -11.95 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(2)]TJ/F3 9.96 Tf 4.38 2.49 TD[(,)]TJ/F5 9.96 Tf 5.81 0 TD[(p)]TJ/F17 6.97 Tf 5.01 3.61 TD[(0)]TJ/F7 6.97 Tf 0 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.81 -0.99 TD[(2)]TJ/F3 9.96 Tf 4.39 3.59 TD[(,)-304(and)]TJ/F5 9.96 Tf 24.81 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F16 4.98 Tf 3.3 -0.99 TD[(2)]TJ/F3 9.96 Tf 7.35 2.49 TD[(in)]TJ/F5 9.96 Tf 11.26 0 TD[(S)]TJ/F7 6.97 Tf 6.11 -1.5 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F16 4.98 Tf 2.81 -0.99 TD[(2)]TJ/F7 6.97 Tf 3.89 0.99 TD[(j)]TJ/F16 4.98 Tf 3.3 -0.99 TD[(2)]TJ/F3 9.96 Tf 7.15 2.49 TD[(=)]TJ/F5 9.96 Tf 10.51 0 TD[(T)]TJ/F3 9.96 Tf 7.21 0 TD[(.)-432(W)83(e)-297(ga)27(v)28(e)-297(the)-298(\257rst)-297(t)26(w)28(o)-297(ab)-27(o)26(v)28(e,)-304(the)-297(latter)-298(t)27(w)28(o)-297(are)-298(giv)27(en)]TJ -129.65 -11.95 TD[(b)27(y)]TJ/F5 9.96 Tf 82.92 -23.92 TD[(p)]TJ/F17 6.97 Tf 5.01 4.11 TD[(0)]TJ/F7 6.97 Tf 0 -6.57 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 4.38 3.46 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(T)]TJ/F3 9.96 Tf 7.21 0 TD[(\))-999(=)-1000(\(cos)]TJ/F10 9.96 Tf 50.41 0 TD[(O)]TJ/F7 6.97 Tf 7.92 -1.49 TD[(T)]TJ/F3 9.96 Tf 8.49 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.79 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F7 6.97 Tf -10.04 -6.57 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(2)]TJ/F5 9.96 Tf 6.26 3.77 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(sin)]TJ/F10 9.96 Tf 13.89 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(T)]TJ/F3 9.96 Tf 8.49 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.79 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(2)]TJ/F7 6.97 Tf -10.04 -6.57 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.88 0.99 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(2)]TJ/F3 9.96 Tf 6.26 3.77 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)]TJ -193.43 -17.16 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.49 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(2)]TJ/F3 9.96 Tf 4.38 2.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(T)]TJ/F3 9.96 Tf 7.21 0 TD[(\))-999(=)]TJ/F5 9.96 Tf 31.54 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.79 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(2)]TJ/F7 6.97 Tf -10.53 -6.56 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(2)]TJ/F5 9.96 Tf 6.75 3.77 TD[(p)]TJ/F17 6.97 Tf 5.01 4.12 TD[(0)]TJ/F7 6.97 Tf 0 -6.58 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(2)]TJ/F5 9.96 Tf 4.39 3.45 TD[(:)]TJ/F3 9.96 Tf -171.87 -26.13 TD[(By)-542(substituting)-544(those)-543(co)-27(ordinates)-544(in)-543(Equation)-543(7.5)-543(w)27(e)-542(obtain)-543(that)]TJ/F5 9.96 Tf 308.87 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.79 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F7 6.97 Tf -10.52 -6.56 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 6.75 3.77 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 10.21 0 TD[(\))-627(=)]TJ/F5 9.96 Tf -344.86 -14.17 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.79 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.88 1 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(2)]TJ/F7 6.97 Tf -10.53 -6.56 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 6.74 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\),)-333(as)-333(claimed.)]TJ ET q 0.691475 0 -0 0.691475 74.93 -341.33 cm /Im76 Do Q BT/F10 9.96 Tf 199.76 -330.01 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(T)]TJ/F5 9.96 Tf -35.82 33.2 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.79 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F7 6.97 Tf 3.88 1 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(2)]TJ/F7 6.97 Tf -10.04 -6.56 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F3 9.96 Tf 6.26 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf -34.81 -41.55 TD[(i)]TJ/F12 6.97 Tf 3.43 -1.5 TD[(1)]TJ/F5 9.96 Tf -95.07 41.56 TD[(j)]TJ/F12 6.97 Tf 4.11 -1.49 TD[(2)]TJ/F5 9.96 Tf 72.59 21.19 TD[(i)]TJ/F12 6.97 Tf 3.43 -1.5 TD[(2)]TJ/F5 9.96 Tf 58.32 11.49 TD[(i)]TJ/F17 6.97 Tf 3.43 3.61 TD[(0)]TJ/F12 6.97 Tf 0 -6.08 TD[(1)]TJ/F3 9.96 Tf -178.22 -106.58 TD[(Figure)-333(7.16:)]TJ/F5 9.96 Tf 56.33 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(2)]TJ/F7 6.97 Tf 3.88 0.99 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf -10.05 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F3 9.96 Tf 5.8 3.77 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-278(=)]TJ/F5 9.96 Tf 17.16 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.43 TD[(i)]TJ/F16 4.98 Tf 2.81 -0.99 TD[(2)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf -10.05 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F7 6.97 Tf 3.88 1 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(2)]TJ/F3 9.96 Tf 5.79 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\).)-444(In)-333(the)-334(picture,)]TJ/F5 9.96 Tf 77.22 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.43 TD[(i)]TJ/F16 4.98 Tf 2.81 -0.99 TD[(2)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf -10.05 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F3 9.96 Tf 5.8 3.77 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf 6.64 0 TD[(<)]TJ/F3 9.96 Tf 10.51 0 TD[(0.)]TJ -299.81 -30.47 TD[(\(ii\))]TJ/F5 9.96 Tf 21.58 0 TD[(j)]TJ/F12 6.97 Tf 4.1 -1.49 TD[(1)]TJ/F3 9.96 Tf 8.82 1.49 TD[(=)]TJ/F5 9.96 Tf 12.11 0 TD[(i)]TJ/F12 6.97 Tf 3.43 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(.)-731(In)-429(this)-430(case,)]TJ/F5 9.96 Tf 68.88 0 TD[(j)]TJ/F3 9.96 Tf 9.03 0 TD[(=)]TJ/F5 9.96 Tf 12.1 0 TD[(i)]TJ/F12 6.97 Tf 3.43 -1.49 TD[(1)]TJ/F3 9.96 Tf 4.47 1.49 TD[(.)-731(Again)-430(w)27(e)-428(start)-429(b)27(y)-429(sho)27(wing)-428(that)]TJ/F5 9.96 Tf 156.74 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.79 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F7 6.97 Tf -10.03 -6.57 TD[(i)]TJ/F16 4.98 Tf 2.81 -0.99 TD[(2)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F3 9.96 Tf 6.26 3.77 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))-437(=)]TJ/F5 9.96 Tf -346.76 -14.17 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.79 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(2)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(2)]TJ/F7 6.97 Tf -10.04 -6.56 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F7 6.97 Tf 3.88 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F3 9.96 Tf 6.26 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\).)-665(F)82(or)-406(an)-407(illustration)-408(of)-407(what)-407(happ)-28(ens)-407(in)-407(screen)]TJ/F5 9.96 Tf 218.74 0 TD[(T)]TJ/F3 9.96 Tf 11.2 0 TD[(=)]TJ/F5 9.96 Tf 11.74 0 TD[(S)]TJ/F7 6.97 Tf 6.1 -1.49 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 4.38 2.49 TD[(,)-425(consult)-407(Figure)]TJ -292.52 -11.95 TD[(7.16.)-748(As)-435(in)-435(the)-434(case)]TJ/F5 9.96 Tf 96.54 0 TD[(j)]TJ/F12 6.97 Tf 4.1 -1.49 TD[(1)]TJ/F3 9.96 Tf 8.92 1.49 TD[(=)]TJ/F5 9.96 Tf 12.2 0 TD[(i)]TJ/F12 6.97 Tf 3.43 -1.49 TD[(1)]TJ/F3 9.96 Tf 8.8 1.49 TD[(it)-434(holds)-435(that)]TJ/F5 9.96 Tf 60.63 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.49 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 4.38 2.49 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))-446(=)]TJ/F10 9.96 Tf 20.52 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(T)]TJ/F3 9.96 Tf 6.27 1.49 TD[(.)-748(Therefore,)]TJ/F5 9.96 Tf 59.41 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.49 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F7 6.97 Tf 3.88 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-447(=)]TJ/F10 9.96 Tf -346.66 -11.95 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.5 TD[(T)]TJ/F3 9.96 Tf 8.57 1.5 TD[(+)]TJ/F5 9.96 Tf 10.04 0 TD[(\274)]TJ/F3 9.96 Tf 6.04 0 TD[(.)-482(Angle)]TJ/F5 9.96 Tf 36.19 0 TD[(\256)]TJ/F7 6.97 Tf 6.38 -1.5 TD[(i)]TJ/F16 4.98 Tf 2.81 -0.99 TD[(2)]TJ/F7 6.97 Tf 3.89 0.99 TD[(j)]TJ/F16 4.98 Tf 3.3 -0.99 TD[(2)]TJ/F3 9.96 Tf 4.38 2.49 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))-298(=)]TJ/F5 9.96 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TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F3 9.96 Tf 6.75 3.77 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(:)]TJ/F3 9.96 Tf -147.24 -25.1 TD[(\(iii\))]TJ/F5 9.96 Tf 24.34 0 TD[(j)]TJ/F12 6.97 Tf 4.1 -1.5 TD[(1)]TJ/F3 9.96 Tf 8.33 1.5 TD[(=)]TJ/F5 9.96 Tf 11.6 0 TD[(i)]TJ/F7 6.97 Tf 3.43 -1.5 TD[(t)]TJ/F5 9.96 Tf 3.5 1.5 TD[(;)-166(t)]TJ/F3 9.96 Tf 11.88 0 TD[(=)-386(3)]TJ/F5 9.96 Tf 16.58 0 TD[(;)-166(:)-167(:)-167(:)-166(m)]TJ/F3 9.96 Tf 26.45 0 TD[(.)-641(In)-398(this)-399(case)]TJ/F5 9.96 Tf 64.06 0 TD[(j)]TJ/F3 9.96 Tf 8.53 0 TD[(=)]TJ/F5 9.96 Tf 11.6 0 TD[(i)]TJ/F12 6.97 Tf 3.43 -1.5 TD[(1)]TJ/F3 9.96 Tf 4.47 1.5 TD[(.)-640(W)82(e)-398(start)-398(b)26(y)-398(analyzing)]TJ/F5 9.96 Tf 111.16 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.78 TD[(i)]TJ/F14 4.98 Tf 2.82 -0.99 TD[(t)]TJ/F7 6.97 Tf 3.3 0.99 TD[(j)]TJ/F16 4.98 Tf 3.3 -0.99 TD[(2)]TJ/F7 6.97 Tf -9.46 -6.57 TD[(i)]TJ/F14 4.98 Tf 2.82 -0.99 TD[(t)]TJ/F7 6.97 Tf 3.31 0.99 TD[(i)]TJ/F16 4.98 Tf 2.81 -0.99 TD[(1)]TJ/F3 9.96 Tf 6.26 3.77 TD[(.)-641(F)82(or)]TJ -339.03 -11.95 TD[(determining)]TJ/F5 9.96 Tf 55.52 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.5 TD[(i)]TJ/F14 4.98 Tf 2.82 -0.99 TD[(t)]TJ/F7 6.97 Tf 3.31 0.99 TD[(i)]TJ/F16 4.98 Tf 2.81 -0.99 TD[(1)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))-348(w)26(e)-348(compute)-349(in)]TJ/F5 9.96 Tf 74.5 0 TD[(T)]TJ/F3 9.96 Tf 10.23 0 TD[(=)]TJ/F5 9.96 Tf 10.78 0 TD[(S)]TJ/F7 6.97 Tf 6.11 -1.5 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.88 0.99 TD[(i)]TJ/F14 4.98 Tf 2.82 -0.99 TD[(t)]TJ/F3 9.96 Tf 7.28 2.49 TD[(co)-27(ordinates)]TJ/F5 9.96 Tf 53.09 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F3 9.96 Tf 4.38 2.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(T)]TJ/F3 9.96 Tf 7.21 0 TD[(\))-303(=)-305(\(0)]TJ/F5 9.96 Tf 26.53 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\),)]TJ/F5 9.96 Tf 15.14 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F16 4.98 Tf 2.81 -0.99 TD[(2)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(T)]TJ/F3 9.96 Tf 7.21 0 TD[(\))-303(=)]TJ -348.09 -11.96 TD[(\(cos)]TJ/F10 9.96 Tf 18.87 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(T)]TJ/F5 9.96 Tf 6.28 1.49 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(sin)]TJ/F10 9.96 Tf 13.89 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(T)]TJ/F3 9.96 Tf 6.27 1.49 TD[(\),)-333(and)]TJ/F5 9.96 Tf -16.64 -22.88 TD[(p)]TJ/F7 6.97 Tf 5.02 -1.5 TD[(i)]TJ/F14 4.98 Tf 2.81 -0.99 TD[(t)]TJ/F3 9.96 Tf 3.81 2.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(T)]TJ/F3 9.96 Tf 7.2 0 TD[(\))-1000(=)]TJ/F5 9.96 Tf 31.54 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.42 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F14 4.98 Tf 2.82 -0.99 TD[(t)]TJ/F7 6.97 Tf -10.05 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.75 3.78 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F4 9.96 Tf 3.88 0 TD[(rot)]TJ/F7 6.97 Tf 14.89 -3.79 TD[(\256)]TJ/F14 4.98 Tf 5.18 3.9 TD[(i)]TJ/F16 4.98 Tf 2.66 -1.5 TD[(1)]TJ/F14 4.98 Tf 3.89 1.5 TD[(i)]TJ 2.65 -1.35 TD[(t)]TJ -9.2 -4.82 TD[(i)]TJ/F16 4.98 Tf 2.66 -1.49 TD[(1)]TJ/F14 4.98 Tf 3.89 1.49 TD[(i)]TJ/F16 4.98 Tf 2.65 -1.49 TD[(2)]TJ/F12 6.97 Tf 5.61 3.76 TD[(\()]TJ/F7 6.97 Tf 3.11 0 TD[(q)]TJ/F12 6.97 Tf 3.9 0 TD[(\))]TJ/F3 9.96 Tf 3.61 3.79 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(2)]TJ/F3 9.96 Tf 4.38 2.49 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)]TJ/F3 9.96 Tf -116.62 -20.58 TD[(=)]TJ/F5 9.96 Tf 17.7 0 TD[(\257)]TJ/F7 6.97 Tf 6.16 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F14 4.98 Tf 2.82 -1 TD[(t)]TJ/F7 6.97 Tf -10.05 -6.2 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.75 3.77 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\)\(cos\()]TJ/F10 9.96 Tf 24.96 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(T)]TJ/F3 9.96 Tf 8.48 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F14 4.98 Tf 2.82 -1 TD[(t)]TJ/F7 6.97 Tf -9.56 -6.2 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\)\))]TJ/F5 9.96 Tf 7.75 0 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(sin\()]TJ/F10 9.96 Tf 16.11 0 TD[(O)]TJ/F7 6.97 Tf 7.92 -1.49 TD[(T)]TJ/F3 9.96 Tf 8.49 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F14 4.98 Tf 2.81 -1 TD[(t)]TJ/F7 6.97 Tf -9.56 -6.2 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\)\)\))]TJ/F5 9.96 Tf 11.62 0 TD[(:)]TJ/F3 9.96 Tf -311.02 -22.89 TD[(Therefore,)]TJ/F5 9.96 Tf 67.73 -21.83 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.49 TD[(i)]TJ/F14 4.98 Tf 2.82 -1 TD[(t)]TJ/F7 6.97 Tf 3.3 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F3 9.96 Tf 4.38 2.49 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-1277(=)]TJ/F15 9.96 Tf 37.07 17.04 TD[(\()]TJ/F10 9.96 Tf 8.03 -10.24 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.5 TD[(T)]TJ/F3 9.96 Tf 8.48 1.5 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.42 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F14 4.98 Tf 2.82 -0.99 TD[(t)]TJ/F7 6.97 Tf -9.56 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.78 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)-2828(\257)]TJ/F7 6.97 Tf 37.1 4.42 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.88 0.99 TD[(i)]TJ/F14 4.98 Tf 2.82 -0.99 TD[(t)]TJ/F7 6.97 Tf -10.05 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.78 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))]TJ/F5 9.96 Tf 9.96 0 TD[(>)]TJ/F3 9.96 Tf 13.83 0 TD[(0)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F10 9.96 Tf -149.85 -14.35 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(T)]TJ/F3 9.96 Tf 8.48 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F14 4.98 Tf 2.82 -0.99 TD[(t)]TJ/F7 6.97 Tf -9.56 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-222(+)]TJ/F5 9.96 Tf 16.05 0 TD[(\274)-35(;)-1000(\257)]TJ/F7 6.97 Tf 24.92 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.88 0.99 TD[(i)]TJ/F14 4.98 Tf 2.82 -0.99 TD[(t)]TJ/F7 6.97 Tf -10.05 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.77 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.81 0 TD[(\))]TJ/F5 9.96 Tf 9.96 0 TD[(<)]TJ/F3 9.96 Tf 13.83 0 TD[(0)]TJ/F5 9.96 Tf 4.98 0 TD[(:)]TJ/F3 9.96 Tf -291.05 -20.8 TD[(W)83(e)-394(use)-394(the)-395(co)-27(ordinates,)]TJ/F5 9.96 Tf 109.8 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(i)]TJ/F14 4.98 Tf 2.81 -0.99 TD[(t)]TJ/F3 9.96 Tf 3.81 2.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\))-379(=)]TJ/F5 9.96 Tf 19.18 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F16 4.98 Tf 3.3 -0.99 TD[(1)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\))-379(=)-380(\(0)]TJ/F5 9.96 Tf 28.03 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\))-394(and)]TJ/F5 9.96 Tf 32.76 0 TD[(p)]TJ/F7 6.97 Tf 5.01 -1.5 TD[(j)]TJ/F16 4.98 Tf 3.29 -0.99 TD[(2)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\))-379(=)-380(\(cos)]TJ/F10 9.96 Tf 38.05 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.5 TD[(S)]TJ/F5 9.96 Tf 5.77 1.5 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(sin)]TJ/F10 9.96 Tf 13.89 0 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.5 TD[(S)]TJ/F3 9.96 Tf 5.77 1.5 TD[(\))-393(in)]TJ/F5 9.96 Tf -346.64 -11.96 TD[(S)]TJ/F3 9.96 Tf 9.45 0 TD[(=)]TJ/F5 9.96 Tf 10.51 0 TD[(S)]TJ/F7 6.97 Tf 6.11 -1.49 TD[(i)]TJ/F14 4.98 Tf 2.82 -1 TD[(t)]TJ/F7 6.97 Tf 3.3 1 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(2)]TJ/F3 9.96 Tf 7.15 2.49 TD[(=)]TJ/F5 9.96 Tf 10.52 0 TD[(S)]TJ/F7 6.97 Tf 6.1 -1.49 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F3 9.96 Tf 7.71 2.49 TD[(for)-332(determining)]TJ/F5 9.96 Tf 70.6 0 TD[(\256)]TJ/F7 6.97 Tf 6.37 -1.49 TD[(i)]TJ/F14 4.98 Tf 2.82 -1 TD[(t)]TJ/F7 6.97 Tf 3.31 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F3 9.96 Tf 4.39 2.49 TD[(\()-74(~)]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\).)-444(F)82(rom)-332(Equation)-334(7.3)-333(it)-333(follo)27(ws)-333(that)]TJ/F10 9.96 Tf -123.58 -32.21 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(S)]TJ/F3 9.96 Tf 18.5 1.49 TD[(=)]TJ/F15 9.96 Tf 20.47 17.03 TD[(\()]TJ/F10 9.96 Tf 8.03 -10.24 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(T)]TJ/F3 9.96 Tf 8.48 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F14 4.98 Tf 2.81 -0.99 TD[(t)]TJ/F7 6.97 Tf -9.56 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-222(+)]TJ/F5 9.96 Tf 16.05 0 TD[(\256)]TJ/F7 6.97 Tf 6.4 4.79 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F7 6.97 Tf -10.51 -6.56 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F3 9.96 Tf 6.26 3.77 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-222(+)]TJ/F5 9.96 Tf 16.05 0 TD[(\274)-36(;)-1000(\257)]TJ/F7 6.97 Tf 24.92 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F7 6.97 Tf 3.89 0.99 TD[(i)]TJ/F14 4.98 Tf 2.81 -0.99 TD[(t)]TJ/F7 6.97 Tf -10.04 -6.21 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf 9.96 0 TD[(>)]TJ/F3 9.96 Tf 13.83 0 TD[(0)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F10 9.96 Tf -197.2 -14.34 TD[(O)]TJ/F7 6.97 Tf 7.93 -1.49 TD[(T)]TJ/F3 9.96 Tf 8.48 1.49 TD[(+)]TJ/F5 9.96 Tf 9.96 0 TD[(\256)]TJ/F7 6.97 Tf 6.41 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F14 4.98 Tf 2.81 -1 TD[(t)]TJ/F7 6.97 Tf -9.56 -6.2 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))-222(+)]TJ/F5 9.96 Tf 16.05 0 TD[(\256)]TJ/F7 6.97 Tf 6.4 4.79 TD[(j)]TJ/F16 4.98 Tf 3.3 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F7 6.97 Tf -10.51 -6.56 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F3 9.96 Tf 6.26 3.77 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)-2827(\257)]TJ/F7 6.97 Tf 37.09 4.43 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F14 4.98 Tf 2.81 -1 TD[(t)]TJ/F7 6.97 Tf -10.04 -6.2 TD[(i)]TJ/F16 4.98 Tf 2.81 -1 TD[(1)]TJ/F7 6.97 Tf 3.89 1 TD[(i)]TJ/F16 4.98 Tf 2.82 -1 TD[(2)]TJ/F3 9.96 Tf 5.74 3.77 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(q)]TJ/F3 9.96 Tf 4.8 0 TD[(\))]TJ/F5 9.96 Tf 9.96 0 TD[(<)]TJ/F3 9.96 Tf 13.83 0 TD[(0)]TJ/F5 9.96 Tf 4.98 0 TD[(:)]TJ/F3 9.96 Tf -305.45 -26.23 TD[(After)-419(subtracting)-420(it)-419(follo)27(ws)-419(that)]TJ/F5 9.96 Tf 147.22 0 TD[(\256)]TJ/F7 6.97 Tf 6.4 4.79 TD[(i)]TJ/F14 4.98 Tf 2.82 -1 TD[(t)]TJ/F7 6.97 Tf 3.31 1 TD[(j)]TJ/F16 4.98 Tf 3.29 -1 TD[(2)]TJ/F7 6.97 Tf -9.45 -6.57 TD[(i)]TJ/F14 4.98 Tf 2.81 -0.99 TD[(t)]TJ/F7 6.97 Tf 3.31 0.99 TD[(i)]TJ/F16 4.98 Tf 2.82 -0.99 TD[(1)]TJ/F3 9.96 Tf 6.26 3.77 TD[(\()-74(~)]TJ/F5 9.96 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TD[(3)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(\))-228(consists)]TJ -323.22 -11.95 TD[(of)-429(the)-428(t)26(w)28(o)-428(comp)-27(onen)26(ts)]TJ ET 0.4 w 86.11 -72.46 m 92.52 -72.46 l S BT/F5 9.96 Tf 86.11 -78.14 TD[(\256)]TJ/F12 6.97 Tf 6.41 -1.5 TD[(12)]TJ/F3 9.96 Tf 8.44 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))-429(and)]TJ/F5 9.96 Tf 28.46 0 TD[(h)]TJ/F12 6.97 Tf 5.74 3.61 TD[(23)]TJ 0 -6.09 TD[(21)]TJ/F3 9.96 Tf 9.8 2.48 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(\).)-730(The)-429(standard)-429(form)-429(of)]TJ/F5 9.96 Tf 114.66 0 TD[(x)]TJ/F3 9.96 Tf 9.97 0 TD[(restricted)-428(to)]TJ/F4 9.96 Tf -308.56 -11.96 TD[(Dom)]TJ/F12 6.97 Tf 24.06 -1.49 TD[(3)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))-374(is)-373(giv)27(en)-373(b)27(y)-373(the)-374(represen)27(tativ)28(es)]TJ/F5 9.96 Tf 144.57 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(12)]TJ/F3 9.96 Tf 8.44 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))-345(=)]TJ/F7 6.97 Tf 19.69 3.93 TD[(\274)]TJ ET 0.4 w 206.88 -87.61 m 211.79 -87.61 l S BT/F12 6.97 Tf 207.35 -93.53 TD[(6)]TJ/F3 9.96 Tf 9.36 3.43 TD[(and)]TJ/F5 9.96 Tf 19.77 0 TD[(\256)]TJ/F12 6.97 Tf 6.41 3.62 TD[(23)]TJ -0.04 -6.09 TD[(21)]TJ/F3 9.96 Tf 9.83 2.47 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\))-345(=)]TJ/F10 9.96 Tf 18.5 0 TD[(\241)]TJ/F12 6.97 Tf 8.94 3.93 TD[(5)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 289.69 -87.61 m 298.57 -87.61 l S BT/F12 6.97 Tf 290.16 -93.53 TD[(12)]TJ/F3 9.96 Tf 9.6 3.43 TD[(,)-383(compare)]TJ -319.6 -11.95 TD[(De\257nition)-281(7.33.)-428(The)-281(\257b)-28(er)]TJ/F5 9.96 Tf 112.99 0 TD[(f)]TJ/F17 6.97 Tf 5.95 3.62 TD[(\241)]TJ/F12 6.97 Tf 6.22 0 TD[(1)]TJ/F3 9.96 Tf 4.47 -3.62 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(\))-281(consists)-281(exactly)-282(of)-282(those)-281(p)-28(oin)27(ts)-281(in)]TJ/F6 9.96 Tf 153.53 0 TD[(FM)]TJ/F12 6.97 Tf 15.64 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.46 1.49 TD[(\(3\))-282(that)-281(are)]TJ -312.83 -11.95 TD[(mapp)-28(ed)-321(on)-320(the)-321(same)-321(standard)-321(form)-321(in)]TJ/F6 9.96 Tf 169.73 0 TD[(XAH)]TJ/F7 6.97 Tf 22.41 -1.49 TD[(n)]TJ/F3 9.96 Tf 5.42 1.49 TD[(.)-440(W)82(e)-320(obtain)-321(these)-321(p)-27(oin)26(ts)-320(b)27(y)-320(analyzing)]TJ -197.56 -11.95 TD[(the)-387(four)-386(distinct)-387(represen)27(tativ)27(es)-385(for)]TJ/F5 9.96 Tf 159.81 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(12)]TJ/F3 9.96 Tf 12.29 1.49 TD[(and)]TJ/F5 9.96 Tf 19.9 0 TD[(\256)]TJ/F12 6.97 Tf 6.41 3.61 TD[(23)]TJ -0.04 -6.08 TD[(21)]TJ/F3 9.96 Tf 9.84 2.47 TD[(.)-604(Cho)-28(ose)-387(for)-387(example)]TJ/F5 9.96 Tf 99.28 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(12)]TJ/F3 9.96 Tf 12.09 1.49 TD[(=)]TJ/F10 9.96 Tf 11.4 0 TD[(\241)]TJ/F12 6.97 Tf 8.94 3.92 TD[(5)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 332.82 -123.46 m 341.7 -123.46 l S BT/F12 6.97 Tf 335.28 -129.39 TD[(6)]TJ/F3 9.96 Tf -355.12 -8.51 TD[(and)]TJ/F5 9.96 Tf 20.19 0 TD[(\256)]TJ/F12 6.97 Tf 6.41 3.61 TD[(23)]TJ -0.03 -6.08 TD[(21)]TJ/F3 9.96 Tf 13.97 2.47 TD[(=)]TJ/F10 9.96 Tf 11.89 0 TD[(\241)]TJ/F12 6.97 Tf 8.94 3.92 TD[(5)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 41.53 -135.41 m 50.41 -135.41 l S BT/F12 6.97 Tf 42 -141.34 TD[(12)]TJ/F3 9.96 Tf 9.6 3.44 TD[(.)-693(It)-416(follo)27(ws)-415(from)-416(the)-416(nest)-416(structure)-416(that)]TJ/F5 9.96 Tf 185.01 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(13)]TJ/F3 9.96 Tf 12.58 1.5 TD[(=)]TJ/F5 9.96 Tf 11.88 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(12)]TJ/F3 9.96 Tf 8.44 1.5 TD[(,)-437(while)]TJ/F5 9.96 Tf 33.95 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(23)]TJ/F3 9.96 Tf 12.58 1.5 TD[(=)]TJ/F5 9.96 Tf -354.99 -11.95 TD[(\256)]TJ/F12 6.97 Tf 6.41 3.61 TD[(23)]TJ -0.04 -6.09 TD[(21)]TJ/F3 9.96 Tf 12.07 2.48 TD[(+)]TJ/F5 9.96 Tf 9.98 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.5 TD[(21)]TJ/F3 9.96 Tf 11.24 1.5 TD[(=)]TJ/F10 9.96 Tf 10.56 0 TD[(\241)]TJ/F12 6.97 Tf 8.94 3.92 TD[(5)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 45.69 -147.36 m 54.57 -147.36 l S BT/F12 6.97 Tf 48.14 -153.29 TD[(6)]TJ/F3 9.96 Tf 9.85 3.44 TD[(+)]TJ/F7 6.97 Tf 11.17 3.92 TD[(\274)]TJ ET 0.4 w 69.16 -147.36 m 74.07 -147.36 l S BT/F12 6.97 Tf 69.63 -153.29 TD[(6)]TJ/F3 9.96 Tf 8.44 3.44 TD[(=)]TJ/F10 9.96 Tf 10.56 0 TD[(\241)]TJ/F7 6.97 Tf 8.94 3.92 TD[(\274)]TJ ET 0.4 w 97.57 -147.36 m 102.48 -147.36 l S BT/F12 6.97 Tf 98.04 -153.29 TD[(4)]TJ/F3 9.96 Tf 5.63 3.44 TD[(.)-452(The)-335(four)-336(p)-28(oin)27(ts)]TJ/F5 9.96 Tf 78.53 0 TD[(f)]TJ/F12 6.97 Tf 4.87 -1.5 TD[(1)]TJ/F5 9.96 Tf 4.47 1.5 TD[(;)-166(:)-167(:)-167(:)-166(;)-167(f)]TJ/F12 6.97 Tf 27.01 -1.5 TD[(4)]TJ/F3 9.96 Tf 7.81 1.5 TD[(in)]TJ/F6 9.96 Tf 11.65 0 TD[(FM)]TJ/F12 6.97 Tf 15.63 -1.5 TD[(2)]TJ/F3 9.96 Tf 4.47 1.5 TD[(\(3\))-335(obtained)-336(in)-336(this)]TJ -277.95 -11.96 TD[(w)27(a)28(y)-333(with)-333(co)-28(ordinates)-333(\()]TJ/F5 9.96 Tf 99.69 0 TD[(\256)]TJ/F12 6.97 Tf 6.37 -1.49 TD[(12)]TJ/F5 9.96 Tf 8.43 1.49 TD[(;)-167(\256)]TJ/F12 6.97 Tf 10.8 -1.49 TD[(13)]TJ/F5 9.96 Tf 8.44 1.49 TD[(;)-166(\256)]TJ/F12 6.97 Tf 10.8 -1.49 TD[(23)]TJ/F5 9.96 Tf 8.44 1.49 TD[(;)-166(\257)]TJ/F12 6.97 Tf 10.58 3.62 TD[(13)]TJ -0.52 -6.09 TD[(12)]TJ/F5 9.96 Tf 10.32 2.47 TD[(;)-166(\257)]TJ/F12 6.97 Tf 10.59 3.62 TD[(21)]TJ -0.53 -6.09 TD[(23)]TJ/F5 9.96 Tf 10.33 2.47 TD[(;)-166(\257)]TJ/F12 6.97 Tf 10.58 3.62 TD[(31)]TJ -0.52 -6.09 TD[(32)]TJ/F3 9.96 Tf 10.32 2.47 TD[(\),)-333(are)-333(giv)27(en)-333(b)27(y)]TJ/F5 9.96 Tf -101.59 -21.22 TD[(f)]TJ/F12 6.97 Tf 4.88 -1.5 TD[(1)]TJ/F3 9.96 Tf 14.43 1.5 TD[(=)-999(\()]TJ/F7 6.97 Tf 22.77 3.92 TD[(\274)]TJ ET 0.4 w 134.77 -180.54 m 139.68 -180.54 l S BT/F12 6.97 Tf 135.24 -186.47 TD[(6)]TJ/F5 9.96 Tf 5.64 3.44 TD[(;)]TJ/F7 6.97 Tf 5.62 3.92 TD[(\274)]TJ ET 0.4 w 146.5 -180.54 m 151.41 -180.54 l S BT/F12 6.97 Tf 146.97 -186.47 TD[(6)]TJ/F5 9.96 Tf 5.63 3.44 TD[(;)]TJ/F12 6.97 Tf 5.62 3.92 TD[(3)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 158.22 -180.54 m 167.1 -180.54 l S BT/F12 6.97 Tf 160.68 -186.47 TD[(4)]TJ/F5 9.96 Tf 7.62 3.44 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(1)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\))]TJ/F5 9.96 Tf 8.85 0 TD[(;)]TJ -107.7 -14.79 TD[(f)]TJ/F12 6.97 Tf 4.88 -1.49 TD[(2)]TJ/F3 9.96 Tf 14.43 1.49 TD[(=)-999(\()]TJ/F7 6.97 Tf 22.77 3.92 TD[(\274)]TJ ET 0.4 w 134.77 -195.33 m 139.68 -195.33 l S BT/F12 6.97 Tf 135.24 -201.26 TD[(6)]TJ/F5 9.96 Tf 5.64 3.44 TD[(;)]TJ/F7 6.97 Tf 5.62 3.92 TD[(\274)]TJ ET 0.4 w 146.5 -195.33 m 151.41 -195.33 l S BT/F12 6.97 Tf 146.97 -201.26 TD[(6)]TJ/F5 9.96 Tf 5.63 3.44 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F7 6.97 Tf 8.94 3.92 TD[(\274)]TJ ET 0.4 w 165.97 -195.33 m 170.88 -195.33 l S BT/F12 6.97 Tf 166.44 -201.26 TD[(4)]TJ/F5 9.96 Tf 5.63 3.44 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(1)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(0\))]TJ/F5 9.96 Tf 8.86 0 TD[(;)]TJ -111.48 -14.83 TD[(f)]TJ/F12 6.97 Tf 4.88 -1.5 TD[(3)]TJ/F3 9.96 Tf 14.43 1.5 TD[(=)-999(\()]TJ/F10 9.96 Tf 21.58 0 TD[(\241)]TJ/F12 6.97 Tf 8.94 3.92 TD[(5)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 142.52 -210.16 m 151.4 -210.16 l S BT/F12 6.97 Tf 144.97 -216.09 TD[(6)]TJ/F5 9.96 Tf 7.62 3.44 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F12 6.97 Tf 8.94 3.92 TD[(5)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 165.96 -210.16 m 174.84 -210.16 l S BT/F12 6.97 Tf 168.42 -216.09 TD[(6)]TJ/F5 9.96 Tf 7.61 3.44 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F7 6.97 Tf 8.94 3.92 TD[(\274)]TJ ET 0.4 w 189.4 -210.16 m 194.31 -210.16 l S BT/F12 6.97 Tf 189.87 -216.09 TD[(4)]TJ/F5 9.96 Tf 5.64 3.44 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(1)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\))]TJ/F5 9.96 Tf 8.85 0 TD[(;)]TJ -134.91 -14.84 TD[(f)]TJ/F12 6.97 Tf 4.88 -1.49 TD[(4)]TJ/F3 9.96 Tf 14.43 1.49 TD[(=)-999(\()]TJ/F10 9.96 Tf 21.58 0 TD[(\241)]TJ/F12 6.97 Tf 8.94 3.92 TD[(5)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 142.52 -225 m 151.4 -225 l S BT/F12 6.97 Tf 144.97 -230.92 TD[(6)]TJ/F5 9.96 Tf 7.62 3.43 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F12 6.97 Tf 8.94 3.92 TD[(5)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 165.96 -225 m 174.84 -225 l S BT/F12 6.97 Tf 168.42 -230.92 TD[(6)]TJ/F5 9.96 Tf 7.61 3.43 TD[(;)]TJ/F12 6.97 Tf 5.63 3.92 TD[(3)]TJ/F7 6.97 Tf 3.97 0 TD[(\274)]TJ ET 0.4 w 181.66 -225 m 190.53 -225 l S BT/F12 6.97 Tf 184.11 -230.92 TD[(4)]TJ/F5 9.96 Tf 7.62 3.43 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(1)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(0)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(0\))]TJ/F5 9.96 Tf 8.85 0 TD[(:)]TJ/F4 9.96 Tf -243.66 -20.83 TD[(Remark)-383(7.67)]TJ/F3 9.96 Tf 0 -11.95 TD[(In)-277(Chapter)-277(5)-278(w)27(e)-276(ha)27(v)28(e)-277(encoun)27(tered)-276(a)-277(similar)-278(situation)-277(in)-277(comparing)-277(the)-278(spaces)]TJ/F6 9.96 Tf 336.14 0 TD[(CUA)]TJ/F12 6.97 Tf 22.13 -1.49 TD[(3)]TJ/F3 9.96 Tf -358.27 -10.46 TD[(and)]TJ/F6 9.96 Tf 20.26 0 TD[(CD)27(A)]TJ/F12 6.97 Tf 22 -1.49 TD[(3)]TJ/F3 9.96 Tf 8.68 1.49 TD[(of)-423(undirected)-423(and)-423(directed)-423(angles)-424(on)-423(three)-423(p)-28(oin)27(ts.)-713(Recall)-423(particularly)]TJ -50.94 -11.95 TD[(Examples)-333(5.30)-333(and)-334(5.31.)]TJ 0 -24.35 TD[(W)83(e)-394(can)-395(de\257ne)-395(and)-395(\257ll)]TJ/F5 9.96 Tf 101 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(-sreens)-394(in)]TJ/F6 9.96 Tf 45.63 0 TD[(FM)]TJ/F12 6.97 Tf 15.63 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(n)]TJ/F3 9.96 Tf 5.98 0 TD[(\))-394(as)-395(w)27(ell.)-628(Fix)-395(a)-395(p)-28(oin)27(t)]TJ/F5 9.96 Tf 100.54 0 TD[(x)]TJ/F10 9.96 Tf 9.48 0 TD[(2)]TJ/F6 9.96 Tf 10.43 0 TD[(FM)]TJ/F12 6.97 Tf 15.63 -1.49 TD[(2)]TJ/F3 9.96 Tf 4.47 1.49 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(n)]TJ/F3 9.96 Tf 5.98 0 TD[(\).)-628(The)]TJ -332.68 -11.95 TD[(set)-332(of)-332(v)55(anishing)-331(ratios)]TJ/F5 9.96 Tf 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0 TD[(S)]TJ/F7 6.97 Tf 6.11 -1.49 TD[(i)]TJ/F3 9.96 Tf 3.31 1.49 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)]TJ/F9 9.96 Tf -234.93 -18.24 TD[(and)]TJ/F5 9.96 Tf 103.76 -18.25 TD[(V)]TJ/F7 6.97 Tf 5.81 -1.5 TD[(F)-153(M)]TJ/F3 9.96 Tf 14.96 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(T)]TJ/F3 9.96 Tf 7.21 0 TD[(\))-999(=)]TJ/F15 9.96 Tf 39.54 9.46 TD[([)]TJ/F7 6.97 Tf -8 -21.21 TD[(i)]TJ/F12 6.97 Tf 2.82 0 TD[(=1)]TJ/F7 6.97 Tf 10.08 0 TD[(:::m)]TJ/F5 9.96 Tf 15.82 11.75 TD[(V)]TJ/F7 6.97 Tf 5.81 -1.5 TD[(F)-154(M)]TJ/F3 9.96 Tf 14.97 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F7 6.97 Tf 3.6 -1.5 TD[(i)]TJ/F3 9.96 Tf 3.31 1.5 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(:)]TJ/F9 9.96 Tf -256.21 -30.76 TD[(The)-289(V)76(or)51(onoi)-289(diagr)51(am)]TJ/F5 9.96 Tf 94.45 0 TD[(V)]TJ/F7 6.97 Tf 5.81 -1.5 TD[(F)-153(M)]TJ/F3 9.96 Tf 14.96 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(x)]TJ/F3 9.96 Tf 5.7 0 TD[(\))]TJ/F9 9.96 Tf 6.75 0 TD[(is)-289(the)-290(r)50(o)51(ote)51(d)-288(tr)50(e)51(e)-288(of)-290(al)-51(l)]TJ/F5 9.96 Tf 97.73 0 TD[(V)]TJ/F7 6.97 Tf 5.81 -1.5 TD[(F)-154(M)]TJ/F3 9.96 Tf 14.97 1.5 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(T)]TJ/F3 9.96 Tf 7.21 0 TD[(\))]TJ/F9 9.96 Tf 3.87 0 TD[(,)-303(wher)51(e)]TJ/F5 9.96 Tf 33.52 0 TD[(T)]TJ/F9 9.96 Tf 10.09 0 TD[(runs)-289(over)-289(al)-51(l)]TJ/F5 9.96 Tf -308.61 -11.96 TD[(x)]TJ/F9 9.96 Tf 5.69 0 TD[(-scr)51(e)51(ens.)-448(The)-324(or)50(dering)-323(on)]TJ/F5 9.96 Tf 114.82 0 TD[(V)]TJ/F7 6.97 Tf 5.81 -1.49 TD[(F)-153(M)]TJ/F3 9.96 Tf 14.96 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(T)]TJ/F3 9.96 Tf 7.2 0 TD[(\))]TJ/F9 9.96 Tf 7.1 0 TD[(is)-324(inherite)51(d)-323(fr)50(om)-323(the)-324(or)50(dering)-323(on)-324(the)]TJ/F5 9.96 Tf 160.29 0 TD[(x)]TJ/F9 9.96 Tf 5.69 0 TD[(-scr)50(e)51(ens.)]TJ ET q 0.196473 0 -0 0.196473 61.17 -227.78 cm /Im79 Do Q q 0.196473 0 -0 0.196473 18.66 -341.14 cm /Im80 Do Q q 0.196473 0 -0 0.196473 103.68 -341.14 cm /Im81 Do Q q 0.196473 0 -0 0.196473 231.20 -227.78 cm /Im82 Do Q q 0.196473 0 -0 0.196473 188.69 -341.14 cm /Im83 Do Q q 0.196473 0 -0 0.196473 273.71 -341.14 cm /Im84 Do Q BT/F3 9.96 Tf 74.02 -188.48 TD[(1)]TJ 14.17 -36.84 TD[(2)]TJ 14.17 42.5 TD[(5)]TJ 5.67 -36.84 TD[(6)]TJ -66.6 -113.35 TD[(3)]TJ -15.58 25.5 TD[(7)-2664(12)]TJ 110.52 -28.33 TD[(4)]TJ -28.34 8.5 TD[(8)]TJ 2.83 31.17 TD[(9)]TJ 31.52 -25.51 TD[(10)]TJ -2.83 28.34 TD[(11)1000(11)]TJ 104.51 104.86 TD[(1)]TJ 14.17 -36.84 TD[(2)]TJ 14.16 42.5 TD[(5)]TJ 5.67 -36.84 TD[(6)]TJ -66.59 -113.35 TD[(3)]TJ -15.59 25.5 TD[(7)-2664(12)]TJ 110.52 -28.33 TD[(4)]TJ -28.34 8.5 TD[(8)]TJ 2.84 31.17 TD[(9)]TJ 31.51 -25.51 TD[(10)]TJ -2.83 28.34 TD[(11)18071(11)]TJ ET 0.85 w 51.01 -284.89 m 51.01 -284.04 l S 0.85 w 52.34 -282.41 m 52.34 -281.56 l S 0.85 w 53.67 -279.93 m 53.67 -279.08 l S 0.85 w 54.99 -277.45 m 54.99 -276.6 l S 0.85 w 56.32 -274.97 m 56.32 -274.12 l S 0.85 w 57.65 -272.49 m 57.65 -271.64 l S 0.85 w 58.98 -270.01 m 58.98 -269.16 l S 0.85 w 60.31 -267.53 m 60.31 -266.68 l S 0.85 w 61.64 -265.05 m 61.64 -264.2 l S 0.85 w 62.96 -262.57 m 62.96 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102.75 -220.41 l S 0.85 w 101.84 -218.61 m 101.84 -217.76 l S 0.85 w 100.92 -215.96 m 100.92 -215.11 l S 0.85 w 100.01 -213.31 m 100.01 -212.46 l S 0.85 w 99.09 -210.66 m 99.09 -209.81 l S 0.85 w 98.18 -208.01 m 98.18 -207.16 l S 0.85 w 97.27 -205.36 m 97.27 -204.51 l S 0.85 w 96.35 -202.7 m 96.35 -201.85 l S 0.85 w 221.04 -284.89 m 221.04 -284.04 l S 0.85 w 222.37 -282.41 m 222.37 -281.56 l S 0.85 w 223.7 -279.93 m 223.7 -279.08 l S 0.85 w 225.03 -277.45 m 225.03 -276.6 l S 0.85 w 226.35 -274.97 m 226.35 -274.12 l S 0.85 w 227.68 -272.49 m 227.68 -271.64 l S 0.85 w 229.01 -270.01 m 229.01 -269.16 l S 0.85 w 230.34 -267.53 m 230.34 -266.68 l S 0.85 w 231.67 -265.05 m 231.67 -264.2 l S 0.85 w 233 -262.57 m 233 -261.72 l S 0.85 w 234.32 -260.09 m 234.32 -259.24 l S 0.85 w 235.65 -257.61 m 235.65 -256.76 l S 0.85 w 236.98 -255.13 m 236.98 -254.28 l S 0.85 w 238.31 -252.65 m 238.31 -251.8 l S 0.85 w 239.64 -250.17 m 239.64 -249.32 l S 0.85 w 240.97 -247.69 m 240.97 -246.84 l S 0.85 w 242.29 -245.21 m 242.29 -244.36 l S 0.85 w 243.62 -242.73 m 243.62 -241.88 l S 0.85 w 244.95 -240.25 m 244.95 -239.4 l S 0.85 w 246.28 -237.77 m 246.28 -236.92 l S 0.85 w 247.61 -235.29 m 247.61 -234.44 l S 0.85 w 248.94 -232.81 m 248.94 -231.96 l S 0.85 w 250.26 -230.33 m 250.26 -229.48 l S 0.85 w 251.59 -227.85 m 251.59 -227 l S 0.85 w 252.92 -225.37 m 252.92 -224.52 l S 0.85 w 254.25 -222.9 m 254.25 -222.05 l S 0.85 w 255.58 -220.42 m 255.58 -219.57 l S 0.85 w 256.91 -217.94 m 256.91 -217.09 l S 0.85 w 258.23 -215.46 m 258.23 -214.61 l S 0.85 w 259.56 -212.98 m 259.56 -212.13 l S 0.85 w 260.89 -210.5 m 260.89 -209.65 l S 0.85 w 262.22 -208.02 m 262.22 -207.17 l S 0.85 w 263.55 -205.54 m 263.55 -204.69 l S 0.85 w 294.72 -284.89 m 294.72 -284.04 l S 0.85 w 293.81 -282.23 m 293.81 -281.38 l S 0.85 w 292.89 -279.58 m 292.89 -278.73 l S 0.85 w 291.98 -276.93 m 291.98 -276.08 l S 0.85 w 291.06 -274.28 m 291.06 -273.43 l S 0.85 w 290.15 -271.63 m 290.15 -270.78 l S 0.85 w 289.24 -268.98 m 289.24 -268.13 l S 0.85 w 288.32 -266.33 m 288.32 -265.48 l S 0.85 w 287.41 -263.68 m 287.41 -262.83 l S 0.85 w 286.49 -261.03 m 286.49 -260.18 l S 0.85 w 285.58 -258.38 m 285.58 -257.53 l S 0.85 w 284.66 -255.72 m 284.66 -254.87 l S 0.85 w 283.75 -253.07 m 283.75 -252.22 l S 0.85 w 282.84 -250.42 m 282.84 -249.57 l S 0.85 w 281.92 -247.77 m 281.92 -246.92 l S 0.85 w 281.01 -245.12 m 281.01 -244.27 l S 0.85 w 280.09 -242.47 m 280.09 -241.62 l S 0.85 w 279.18 -239.82 m 279.18 -238.97 l S 0.85 w 278.27 -237.17 m 278.27 -236.32 l S 0.85 w 277.35 -234.52 m 277.35 -233.67 l S 0.85 w 276.44 -231.87 m 276.44 -231.02 l S 0.85 w 275.52 -229.21 m 275.52 -228.36 l S 0.85 w 274.61 -226.56 m 274.61 -225.71 l S 0.85 w 273.69 -223.91 m 273.69 -223.06 l S 0.85 w 272.78 -221.26 m 272.78 -220.41 l S 0.85 w 271.87 -218.61 m 271.87 -217.76 l S 0.85 w 270.95 -215.96 m 270.95 -215.11 l S 0.85 w 270.04 -213.31 m 270.04 -212.46 l S 0.85 w 269.12 -210.66 m 269.12 -209.81 l S 0.85 w 268.21 -208.01 m 268.21 -207.16 l S 0.85 w 267.3 -205.36 m 267.3 -204.51 l S 0.85 w 266.38 -202.7 m 266.38 -201.85 l S BT -8.5 -363.05 TD[(Figure)-343(7.19:)-466(Constructing)]TJ/F5 9.96 Tf 116.6 0 TD[(V)]TJ/F7 6.97 Tf 5.81 -1.49 TD[(F)-153(M)]TJ/F3 9.96 Tf 14.96 1.49 TD[(\()]TJ/F5 9.96 Tf 3.88 0 TD[(x)]TJ/F3 9.96 Tf 5.69 0 TD[(\):)-465(on)-345(the)-344(left,)-347(initialization;)-349(on)-344(the)-344(righ)27(t,)-346(comple-)]TJ -146.94 -11.95 TD[(tion.)]TJ/F4 9.96 Tf 0 -35.44 TD[(Example)-383(7.69)]TJ/F3 9.96 Tf 0 -11.95 TD[(Recall)-255(Example)-257(4.42.)-418(In)-256(this)-256(example)-256(w)26(e)-255(consider)-256(an)-256(ordered)-256(set)-256(of)-256(sites)-256(in)]TJ/F13 9.96 Tf 320.99 0 TD[(R)]TJ/F3 9.96 Tf 7.19 0 TD[([)]TJ/F5 9.96 Tf 2.77 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(])]TJ/F10 9.96 Tf 3.44 0 TD[(\243)]TJ/F13 9.96 Tf 8.42 0 TD[(R)]TJ/F3 9.96 Tf 7.19 0 TD[([)]TJ/F5 9.96 Tf 2.77 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(])]TJ -359.97 -11.96 TD[(giv)27(en)-332(b)27(y)]TJ/F5 9.96 Tf 9.4 -18.24 TD[(S)]TJ/F3 9.96 Tf 6.68 0 TD[(\()]TJ/F5 9.96 Tf 3.87 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))-999(=)-1000(\(\()]TJ/F10 9.96 Tf 39.29 0 TD[(\241)]TJ/F3 9.96 Tf 7.74 0 TD[(6)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(4\))]TJ/F5 9.96 Tf 8.85 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 TD[(\()]TJ/F10 9.96 Tf 3.87 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(2)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F3 9.96 Tf 7.74 0 TD[(6\))]TJ/F5 9.96 Tf 8.86 0 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(\()]TJ/F10 9.96 Tf 3.88 0 TD[(\241)]TJ/F3 9.96 Tf 7.74 0 TD[(1)]TJ/F5 9.96 Tf 4.98 0 TD[(;)]TJ/F10 9.96 Tf 4.43 0 TD[(\241)]TJ/F3 9.96 Tf 7.74 0 TD[(2)]TJ/F10 9.96 Tf 7.2 0 TD[(\241)]TJ/F3 9.96 Tf 9.96 0 TD[(3)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F3 9.96 Tf 3.59 0 TD[(\))]TJ/F5 9.96 Tf 3.88 0 TD[(;)]TJ/F3 9.96 Tf 4.42 0 TD[(\(0)]TJ/F5 9.96 Tf 8.86 0 TD[(;)]TJ/F10 9.96 Tf 4.42 0 TD[(\241)]TJ/F3 9.96 Tf 7.75 0 TD[(3)]TJ/F5 9.96 Tf 4.98 0 TD[(t)]TJ/F3 9.96 Tf 3.6 0 TD[(\))]TJ/F5 9.96 Tf 3.87 0 TD[(;)]TJ/F3 9.96 Tf 4.43 0 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%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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/Type/FontDescriptor
/CapHeight 850
/Ascent 850
/Descent -200
/FontBBox[-32 -250 1048 750]
/FontName/UVXKRV+CMMI10
/ItalicAngle -14.04
/StemV 72
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%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /UVXKRV+CMMI10  def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 178 /epsilon1 put
dup 180 /eta put
dup 181 /theta put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 63 /star put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /NYIQJT+CMMI7  def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 174 /alpha put
dup 177 /delta put
dup 178 /epsilon1 put
dup 188 /pi put
dup 190 /sigma put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 62 /greater put
dup 64 /partialdiff put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 70 /F put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 102 /f put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark

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endobj
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<<
/Type/FontDescriptor
/CapHeight 850
/Ascent 850
/Descent -200
/FontBBox[-55 -250 1289 751]
/FontName/SQQTKV+CMBX7
/ItalicAngle 0
/StemV 127
/FontFile 43 0 R
/Flags 4
>>
endobj
43 0 obj
<<
/Length1 713
/Length2 2290
/Length3 533
/Length 3536
>>
stream
%!PS-AdobeFont-1.1: CMBX7 1.0
%%CreationDate: 1991 Aug 20 16:35:49

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
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%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /ACSZHL+CMTI10  def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding StandardEncoding readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec
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/Type/FontDescriptor
/CapHeight 850
/Ascent 850
/Descent -200
/FontBBox[-29 -960 1116 775]
/FontName/CLUKMP+CMSY10
/ItalicAngle -14.035
/StemV 85
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/Flags 68
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%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CLUKMP+CMSY10  def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 161 /minus put
dup 162 /periodcentered put
dup 163 /multiply put
dup 164 /asteriskmath put
dup 167 /plusminus put
dup 177 /openbullet put
dup 178 /bullet put
dup 180 /equivalence put
dup 183 /lessequal put
dup 184 /greaterequal put
dup 187 /similar put
dup 189 /propersubset put
dup 190 /propersuperset put
dup 192 /greatermuch put
dup 195 /arrowleft put
dup 33 /arrowright put
dup 34 /arrowup put
dup 35 /arrowdown put
dup 36 /arrowboth put
dup 38 /arrowsoutheast put
dup 41 /arrowdblright put
dup 44 /arrowdblboth put
dup 46 /arrowsouthwest put
dup 47 /proportional put
dup 49 /infinity put
dup 50 /element put
dup 52 /triangle put
dup 54 /negationslash put
dup 55 /mapsto put
dup 56 /universal put
dup 57 /existential put
dup 59 /emptyset put
dup 65 /A put
dup 67 /C put
dup 79 /O put
dup 83 /S put
dup 85 /U put
dup 86 /V put
dup 91 /union put
dup 92 /intersection put
dup 94 /logicaland put
dup 95 /logicalor put
dup 102 /braceleft put
dup 103 /braceright put
dup 104 /angbracketleft put
dup 105 /angbracketright put
dup 106 /bar put
dup 107 /bardbl put
dup 110 /backslash put
dup 112 /radical put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
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%!PS-AdobeFont-1.1: CMTT10 1.00B
%%CreationDate: 1992 Apr 26 10:42:42

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTT10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /RLOYXH+CMTT10  def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
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dup 45 /hyphen put
dup 47 /slash put
dup 48 /zero put
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dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 57 /nine put
dup 65 /A put
dup 81 /Q put
dup 82 /R put
dup 99 /c put
dup 100 /d put
dup 101 /e put
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readonly def
/FontBBox{-4 -235 731 800}readonly def
/UniqueID 5000832 def
currentdict end
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%!PS-AdobeFont-1.1: CMMI5 1.100
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% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
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%!PS-AdobeFont-1.1: CMEX10 1.00
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% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
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%!PS-AdobeFont-1.1: CMR5 1.00B
%%CreationDate: 1992 Feb 19 19:55:02

% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.

11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
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end readonly def
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