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 |
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Page 35
... Right angles had been introduced in Definition 10 , and now Euclid was assum- ing that any two such angles , regardless of where they were situated in the plane , were equal . With this behind him , Euclid arrived at by far the most ...
... Right angles had been introduced in Definition 10 , and now Euclid was assum- ing that any two such angles , regardless of where they were situated in the plane , were equal . With this behind him , Euclid arrived at by far the most ...
Page 46
... right angles = 21+ LBGH > L2 + LBGH And here , at last , Euclid invoked Postulate 5 , a result precisely designed for just such a situation . Since 42 + LBGH < 2 right angles , his postulate allowed him to conclude that lines AB and CD ...
... right angles = 21+ LBGH > L2 + LBGH And here , at last , Euclid invoked Postulate 5 , a result precisely designed for just such a situation . Since 42 + LBGH < 2 right angles , his postulate allowed him to conclude that lines AB and CD ...
Page 63
... angles of quadrilaterals in circles are equal to two right angles . = PROOF We begin with cyclic quadrilateral ABCD and draw the two diag- onals AC and BD , as shown in Figure 3.3 . Note that 41 + 42 + LDAB : 2 right angles , since ...
... angles of quadrilaterals in circles are equal to two right angles . = PROOF We begin with cyclic quadrilateral ABCD and draw the two diag- onals AC and BD , as shown in Figure 3.3 . Note that 41 + 42 + LDAB : 2 right angles , since ...
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 | |
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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