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Praise for William Dunham s Journey Through Genius The GreatTheorems of Mathematics "Dunham deftly guides the reader throughthe verbal and logical intricacies of major mathematical questionsand proofs, conveying a splendid sense of how the greatestmathematicians from ancient to modern times presented theirarguments." Ivars Peterson Author, The Mathematical TouristMathematics and Physics Editor, Science News
"It is mathematics presented as a series of works of art; afascinating lingering over individual examples of ingenuity andinsight. It is mathematics by lightning flash." Isaac Asimov
"It is a captivating collection of essays of major mathematicalachievements brought to life by the personal and historicalanecdotes which the author has skillfully woven into the text. Thisis a book which should find its place on the bookshelf of anyoneinterested in science and the scientists who create it." R. L.Graham, AT&T Bell Laboratories
"Come on a time-machine tour through 2,300 years in which Dunhamdrops in on some of the greatest mathematicians in history. Almostas if we chat over tea and crumpets, we get to know them and theirideas ideas that ring with eternity and that offer glimpses intothe often veiled beauty of mathematics and logic. And all the whilewe marvel, hoping that the tour will not stop." Jearl Walker,Physics Department, Cleveland State University Author of The FlyingCircus of Physics
Contents
Preface v
Acknowledgements ix
Chapter 1 Hippocrates' Quadrature of the Lune (ca 440 BC) 1
Chapter 2 Euclid's Proof of the Pythagorean Theorem (ca 300 BC) 27
Chapter 3 Euclid and the Infinitude of Primes (ca 300 BC) 61
Chapter 4 Archimedes' Determination of Circular Area (ca 225 BC) 84
Chapter 5 Heron's Formula for Triangular Area (ca AD 75) 113
Chapter 6 Cardano and the Solution of the Cubic (1545) 133
Chapter 7 A Gem from Isaac Newton (Late 1660s) 155
Chapter 8 The Bernoullis and the Harmonic Series (1689) 184
Chapter 9 The Extraordinary Sums of Leonhard Euler (1734) 207
Chapter 10 A Sampler of Euler's Number Theory (1736) 223
Chapter 11 The Non-Denumerability of the Continuum (1874) 245
Chapter 12 Cantor and the Transfinite Realm (1891) 267
Afterword 285
Chapter Notes 287
References 291
Index 295
