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What is included with this book?
Preface  xv  

xvii  

xviii  

xix  

xxi  

xxii  

xxiii  
How to Use This Book  xxv  

xxvi  

xxvii  

xxviii  
Chapter 0 Historical Strands of Geometry  1  (8)  

1  (2)  

3  (1)  

4  (2)  

6  (3)  
Chapter 1 What Is Straight?  9  (16)  

9  (4)  

13  (4)  

17  (4)  

21  (4)  
Chapter 2 Straightness on Spheres  25  (12)  

25  (3)  

28  (4)  

32  (3)  

35  (1)  

35  (2)  
Chapter 3 What Is an Angle?  37  (6)  

37  (2)  

39  (2)  

41  (2)  
Chapter 4 Straightness on Cylinders and Cones  43  (16)  

44  (2)  

46  (3)  

49  (1)  

50  (1)  

51  (1)  

51  (2)  

53  (2)  

55  (1)  

56  (1)  

57  (2)  
Chapter 5 Straightness on  59  (14)  



59  (3)  

62  (2)  

64  (2)  

66  

63  (5)  

68  (3)  

71  (1)  

71  (2)  
Chapter 6 Triangles and Congruencies  73  (16)  

73  (1)  

74  (1)  

75  (1)  

76  (2)  

78  (1)  

79  (1)  

80  (5)  

85  (4)  
Chapter 7 Area and Holonomy  89  (20)  

90  (1)  

91  (4)  

95  (1)  

96  (2)  

98  (2)  

100  (2)  

102  (1)  

103  (3)  

106  (3)  
Chapter 8 Parallel Transport  109  (8)  

109  (2)  

111  (3)  

114  (1)  

115  (2)  
Chapter 9 SSS, ASS, SAA, and AAA  117  (8)  

117  (2)  

119  (2)  

121  (2)  

123  (2)  
Chapter 10 Parallel Postulates  125  (18)  

125  (1)  

126  (2)  

128  (2)  

130  (1)  

131  (3)  

134  (2)  

136  (2)  

138  (2)  

140  (3)  
Chapter 11 Isometries and Patterns  143  (22)  

144  (4)  

148  (1)  

149  (4)  

153  (1)  

154  (4)  

158  (1)  

159  (1)  

159  (1)  

160  (1)  

161  (2)  

163  (2)  
Chapter 12 Dissection Theory  165  (12)  

165  (2)  

167  (1)  

168  (1)  

169  (1)  

170  (1)  

171  (1)  

172  (1)  

173  (4)  
Chapter 13 Square Roots, Pythagoras, and Similar Triangles  177  (20)  

178  (1)  

179  (5)  

184  (5)  

189  (1)  

190  (1)  

191  (2)  

193  (1)  

194  (1)  

195  (2)  
Chapter 14 Projections of a Sphere onto a Plane  197  (8)  

198  (1)  

198  (1)  

199  (1)  

200  (2)  

202  (3)  
Chapter 15 Circles  205  (12)  

206  (2)  

208  (4)  

212  (1)  

213  (4)  
Chapter 16 Inversions in Circles  217  (16)  

217  (1)  

218  (3)  

221  (3)  

224  (2)  

226  (4)  

230  (3)  
Chapter 17 Projections (Models) of Hyperbolic Planes  233  (12)  

234  (2)  

236  (1)  

237  (2)  

239  (2)  

241  (1)  

242  (2)  

244  (1)  
Chapter 18 Geometric 2Manifolds  245  (22)  

246  (5)  

251  (2)  

253  (3)  

256  (2)  

258  (5)  

263  (1)  

264  (1)  

265  (2)  
Chapter 19 Geometric Solutions of Quadratic and Cubic Equations  267  (18)  

268  (4)  

272  (4)  

276  (4)  

280  (2)  

282  (3)  
Chapter 20 Trigonometry and Duality  285  (14)  

285  (2)  

287  (3)  

290  (2)  

292  (1)  

293  (1)  

294  (1)  

294  (2)  

296  (1)  

297  (2)  
Chapter 21 Mechanisms  299  (20)  

299  (4)  

303  (4)  

307  (3)  

310  (4)  

314  (3)  

317  (2)  
Chapter 22 3Spheres and Hyperbolic 3Spaces  319  (16)  

320  (2)  

322  (3)  

325  (3)  

328  (2)  

330  (2)  

332  (1)  

333  (2)  
Chapter 23 Polyhedra  335  (8)  

335  (1)  

336  (2)  

338  (1)  

339  (1)  

339  (1)  

340  (3)  
Chapter 24 3Manifolds  The Shape of Space  343  (20)  

344  (3)  

347  (2)  

349  (4)  

353  (2)  

355  (1)  

356  (4)  

360  (1)  

361  (2)  
Appendix A Euclid's Definitions, Postulates, and Common Notions  363  (4)  

363  (3)  

366  (1)  

366  (1)  
Appendix B Constructions of  

367  (1)  

367  (1)  

368  (3)  

371  (1)  

371  (1)  

372  (3)  
Bibliography  375  (10)  
Index  385 