Journey Through Genius: The Great Theorems of MathematicsLike masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve. Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity. “It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov |
Contents
Hippocrates Quadrature of the Lune ca 440 B C | 1 |
Euclids Proof of the Pythagorean Theorem ca 300 B C | 27 |
Euclid and the Infinitude of Primes ca 300 B C | 61 |
Copyright | |
12 other sections not shown
Other editions - View all
Common terms and phrases
appeared Archimedes argument binomial Book calculus Cardano Carl Friedrich Gauss century Chapter circle circle's circumference classical Common Notion compass and straightedge congruent construct continuum hypothesis course cube decimal place definition denumerable depressed cubic diameter discovery divides evenly divisor Elements Epilogue equal equation Euclid Eudoxus excerpt fact factor Fauvel and Gray Fermat finite formula Gauss genius geometry Georg Cantor Greek harmonic series Heath Heron Heron's formula Hippocrates infinite series inscribed instance irrational Isaac Newton Jakob Johann Bernoulli Leibniz length Leonhard Euler likewise logical lune matching mathe mathematicians modern natural numbers non-Euclidean noted number theory one-to-one correspondence parallel postulate Penguin perfect numbers polynomial problem proof Proposition proved Pythagorean theorem quadrature radius rational real numbers regular polygons result right angles right triangle segment semicircle sides simple solid solution solving sphere square straight line subset Tartaglia tion triangle's whole number