List of Figures 1.1 A cubic curve in tropical geometry.. . . . . . . . . . . . . . . 14 2.1 A closed system of mirrors . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Grinding a plane mirror. . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3 What different nations eat and drink. . . . . . . . . . . . . 34 2.4 Vision vs. “inverse vision”. . . . . . . . . . . . . . . . . . . . . . . 35 2.5 Horses by Nadia, at age of 3 years 5 months. . . . . . 35 2.6 Horses from Chauvet Cave (Ardeche) . . . . . . . . . . . . 36 2.7 A symbolic human and a naturalistic bull. . . . . . . . 37 2.8 The icosahedron inscribed into the cube. . . . . . . . . . 38 2.9 The root system D3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.10 From Kepler’s Mysterium Cosmographicum . . . . . . 40 2.11 The root systems D2 and A1 ⊕ A1. . . . . . . . . . . . . . . . 40 3.1 The Palindrome Representation Theorem.. . . . . . . . 51 3.2 Stasheff’s associahedron. . . . . . . . . . . . . . . . . . . . . . . . 57 4.1 Electrolocation in fish.. . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.2 Convex and non-convex sets. . . . . . . . . . . . . . . . . . . . . 77 4.3 An impossible object. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.4 The Magpie on the Gallows . . . . . . . . . . . . . . . . . . . . . 79 4.5 Spherical stone vase, Ancient Egypt . . . . . . . . . . . . . 80 5.1 A tessellation of the sphere. . . . . . . . . . . . . . . . . . . . . . 90 5.2 A hyperbolic tessellation. . . . . . . . . . . . . . . . . . . . . . . . 91 5.3 Euclidean tessellations . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.4 A pattern of angels and devils based on M. C. Escher’s Circle Limit IV and the tessellation {4, 5}. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.5 The underlying Circle Limit IV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.6 The railway tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.7 Paradisio, by Gustave Dor´ . . . . . . . . . . . . . . . . . . . . . 106 xxiii tessellation of M. C. Escher’s
Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2010 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.
