Mathematics and the Imagination

Edward Kasner, James Newman

• Verlag: Dover Publications
• Jahr: 2013
• ISBN:
  9780486320274
• Thema: Mathematik
• Thema: Spiele in der Mathematik

You don’t have to love math to enjoy a hand of cards, a night at the casino, or a puzzle. But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.
A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.
Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting.` — Saturday Review of Literature.

Index

Abbott, Edwin Abbott, 128, 363

Abel, Niels Henrik, 17

Advanced Calculus, 298

Absolute rest, 24

Absolute zero, 24

Acceleration, 301, 326, 342–343

Achilles and the tortoise paradox, 37, 38, 57–58, 62

Ahrens, Wilhelm Ernst Martin Georg, 189, 191, 363

Air-raid casualties, statistics of, 262–263

Alcuin, 159

d’Alembert, Jean le Rond, 246

Aleph-Null, 45, 54

Alephs, 45, 46–47, 62, 63

Alexander of Macedon, 343

Algebraic equations with integer

coefficients, 6, 49, 64, 71, 79, 84,109, 111

Algebraic invariant, 298

Algebraic numbers, 49, 50, 110

Alte Probleme—Neue Lösungen,219

American Journal of Mathematics, The, 178, 191

American Mathematical Monthly, 363, 364

Amusements in Mathematics, 189

Analysis situs, 266 271–274, 287

Analytical geometry, 95–99, 103,120–123, 305, 306, 314

Analytical Theory of Heat, The, 254

Analytic theory of probability, 240

Annals of Mathematics,191

Anthropology, statistics in, 260–261

Anti-snowflake curve, 348–351

Apollo, 71

Apollonius, 12, 13

Applied mathematics, 114, 116, 150, 151

Approximation, methods of, 318,333–334, 336–337

Arabs, 17, 185

Arago, Dominique Francois Jean, 190

Archimedean number (see π), 75

Archimedes, 33–34, 69, 74, 310, 331

Architecture of the Universe, The, 367

Area under a curve, 335–339

Argand, ...