The author of Did Adam and Eve Have Navels? presents a selection of the finest pieces from his Scientific American "Mathematical Games" column, presenting a wide range of mind-bending mathematical puzzles and concepts that range from arithmetic and geometrical games to the meaning of M. C. Escher's artwork. 17,500 first printing No amateur or math authority can be without this ultimate compendium from America's best-loved mathematical expert. Preface xi I Arithmetic and Algebra The Monkey and the Coconuts 3(7) The Calculus of Finite Differences 10(13) Palindromes: Words and Numbers 23(12) II Plane Geometry Curves of Constant Width 35(11) Rep-Tiles 46(13) Piet Hein's Superellipse 59(14) Penrose Tiles 73(21) The Wonders of a Planiverse 94(23) III Solid Geometry and Higher Dimensions The Helix 117(11) Packing Spheres 128(9) Spheres and Hyperspheres 137(13) The Church of the Fourth Dimension 150(12) Hypercubes 162(13) Non-Euclidean Geometry 175(14) IV Symmetry Rotations and Reflections 189(9) The Amazing Creations of Scott Kim 198(14) The Art of M. C. Escher 212(15) V Topology Klein Bottles and Other Surfaces 227(12) Knots 239(15) Doughnuts: Linked and Knotted 254(19) VI Probability Probability and Ambiguity 273(13) Nontransitive Dice and Other Paradoxes 286(11) More Nontransitive Paradoxes 297(18) VII Infinity Infinite Regress 315(12) Aleph-Null and Aleph-One 327(13) Supertasks 340(10) Fractal Music 350(19) Surreal Numbers 369(16) VIII Combinatorics Hexaflexagons 385(13) The Soma Cube 398(11) The Game of Life 409(14) Paper Folding 423(14) Ramsey Theory 437(18) Bulgarian Solitaire and Other Seemingly Endless Tasks 455(16) IX Games and Decision Theory A Matchbox Game-Learning Machine 471(14) Sprouts and Brussels Sprouts 485(8) Harary's Generalized Ticktacktoe 493(11) The New Eleusis 504(13) X Physics Time Travel 517(14) Does Time Ever Stop? 531(10) Induction and Probability 541(12) Simplicity 553(14) XI Logic and Philosophy The Unexpected Hanging 567(13) Newcomb's Paradox 580(12) Nothing 592(18) Everything 610(17) XII Miscellaneous Melody-Making Machines 627(13) Mathematical Zoo 640(20) Godel, Escher, Bach 660(14) Six Sensational Discoveries 674(21) Selected Titles by the Author on Mathematics 695(2) Index 697