Description
Book SynopsisPraise for William Dunham s Journey Through Genius The Great Theorems of Mathematics Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments.
Table of ContentsPreface 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
