Index

1-forms, 98

2-adic metric, 23

Abelian, 43

aﬃne automorphisms, 221

angle, 87

angle deficit, 209

antipodal points, 69

area preserving maps, 219

atlas, 136

Banach–Tarski Theorem, 17, 275

basepoint, 46, 48

basic reflection, 105

basic rotation, 105

bijection, 21

billiards, 213

binary icosahedral group, 63

Bolyai-Gerwein Theorem, 96

Bolzano-Weierstrass Theorem, 72

boundary, 23

Cauchy Integral Formula, 163, 165,

167

Cauchy Rigidity Theorem, 17, 295

Cauchy sequence, 154

Cauchy’s Arm Lemma, 302

Cauchy’s Theorem, 165

Cauchy-Riemann equations, 165

Cauchy-Schwarz inequality, 87

Cayley’s Theorem, 44

chain, 32

chain rule, 164

circle, 56, 116

circular polygon, 166

classification of isometries, 130

classification of surfaces, 36

Clean Dissections, 292

closed set, 23

closure, 23

combinatorial Gauss–Bonnet

Theorem, 209

compact, 26, 36

compact Riemann surfaces, 203

complex analysis, 11

complex analytic function, 163

composing loops, 46

composition, 24

cone surface, 13

connect sum, 36

continued fractions, 241, 245

continuity, 24

convex geodesic polygon, 145

convexity, 110

coordinate chart, 136

covering group, 66

covering space, 8, 65

curve, 133

cylinder, 34

cylinder decomposition, 234

311