Journey through Genius: Great Theorems of MathematicsPraise 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
Hippocrates Quadrature of the Lune ca 440 B C | 1 |
Euclids Proof of the Pythagorean Theorem ca 300 B C | 27 |
Archimedes Determination of Circular Area ca 225 B C | 84 |
On the Sphere and the Cylinder | 99 |
Epilogue | 106 |
Herons Formula for Triangular Area ca A D 75 | 113 |
Cardano and the Solution of the Cubic 1545 | 133 |
A Gem from Isaac Newton Late 1660s | 155 |
The Extraordinary Sums of Leonhard Euler 1734 | 207 |
A Sampler of Eulers Number Theory 1736 | 223 |
The NonDenumerability of the Continuum 1874 | 245 |
Cantor and the Transfinite Realm 1891 | 267 |
AFTERWORD | 285 |
REFERENCES | 291 |
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Common terms and phrases
Archimedes argument binomial Book calculus Cardano Carl Friedrich Gauss century Chapter circle circle's CIRCULAR AREA circumference compass and straightedge congruent construct continuum continuum hypothesis course cube definition denumerable depressed cubic DETERMINATION OF CIRCULAR diameter discovery divides evenly divisor Dunham Elements Epilogue equal equation Euclid EUCLID'S PROOF Eudoxus excerpt fact factor Fermat finite Gauss GEM FROM ISAAC geometry Georg Cantor Greek harmonic series Heath HERON'S FORMULA Hippocrates infinite series INFINITUDE OF PRIMES inscribed instance irrational Isaac Newton Jakob Johann Bernoulli JOURNEY THROUGH GENIUS Leibniz length Leonhard Euler likewise logical lune matching mathe mathematicians modern NON-DENUMERABILITY non-Euclidean noted one-to-one correspondence parallel postulate perfect numbers polynomial problem 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