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by David S. Richeson
Euler's Gem
Cover
Half title
Title
Copyright
Dedication
Contents
Preface
Introduction
Chapter 1 Leonhard Euler and His Three “Great” Friends
Chapter 2 What Is a Polyhedron?
Chapter 3 The Five Perfect Bodies
Chapter 4 The Pythagorean Brotherhood and Plato’s Atomic Theory
Chapter 5 Euclid and His Elements
Chapter 6 Kepler’s Polyhedral Universe
Chapter 7 Euler’s Gem
Chapter 8 Platonic Solids, Golf Balls, Fullerenes, and Geodesic Domes
Chapter 9 Scooped by Descartes?
Chapter 10 Legendre Gets It Right
Chapter 11 A Stroll through Königsberg
Chapter 12 Cauchy’s Flattened Polyhedra
Chapter 13 Planar Graphs, Geoboards, and Brussels Sprouts
Chapter 14 It’s a Colorful World
Chapter 15 New Problems and New Proofs
Chapter 16 Rubber Sheets, Hollow Doughnuts, and Crazy Bottles
Chapter 17 Are They the Same, or Are They Different?
Chapter 18 A Knotty Problem
Chapter 19 Combing the Hair on a Coconut
Chapter 20 When Topology Controls Geometry
Chapter 21 The Topology of Curvy Surfaces
Chapter 22 Navigating in n Dimensions
Chapter 23 Henri Poincaré and the Ascendance of Topology
Epilogue The Million-Dollar Question
Acknowledgements
Appendix A Build Your Own Polyhedra and Surfaces
Appendix B Recommended Readings
Notes
References
Illustrations Credits
Index
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Copyright
E
ULER
’
S
G
EM
T
HE
P
OLYHEDRON
F
ORMULA
AND THE
B
IRTH OF
T
OPOLOGY
D
AVID
S. R
ICHESON
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