The history of geometry in relation to space discusses the contributions of Pythagoras, the advent of Albert Einstein's fourth dimension, and the discovery of seven more dimensions by Princeton mathematician Edward Witten. Introduction ix I The Story of Euclid The First Revolution 3(1) The Geometry of Taxation 4(7) Among the Seven Sages 11(6) The Secret Society 17(12) Euclid's Manifesto 29(10) A Beautiful Woman, a Library, and the End of Civilization 39(14) II The Story of Descartes The Revolution in Place 53(2) The Origin of Latitude and Longitude 55(5) The Legacy of the Rotten Romans 60(10) The Discreet Charm of the Graph 70(9) A Soldier's Story 79(11) Iced by the Snow Queen 90(5) III The Story of Gauss The Curved Space Revolution 95(3) The Trouble with Ptolemy 98(9) A Napoleonic Hero 107(8) The Fall of the Fifth Postulate 115(6) Lost in Hyperbolic Space 121(6) Some Insects Called the Human Race 127(9) A Tale of Two Aliens 136(7) After 2,000 Years, a Face-lift 143(10) IV The Story of Einstein Revolution at the Speed of Light 153(4) Relativity's Other Albert 157(6) The Stuff of Space 163(13) Probationary Technical Expert, Third Class 176(6) A Relatively Euclidean Approach 182(11) Einstein's Apple 193(12) From Inspiration to Perspiration 205(5) Blue Hair Triumphs 210(7) V The Story of Witten The Weird Revolution 217(2) Ten Things I Hate About Your Theory 219(4) The Necessary Uncertainty of Being 223(5) Clash of the Titans 228(3) A Message in a Kaluza-Klein Bottle 231(4) The Birth of Strings 235(4) Particles, Schmarticles! 239(10) The Trouble with Strings 249(6) The Theory Formerly Known as Strings 255(8) Epilogue 263(4) Notes 267(26) Acknowledgments 293(2) Index 295