9780691152820

The Universe in Zero Words

by
  • ISBN13:

    9780691152820

  • ISBN10:

    0691152829

  • Format: Hardcover
  • Copyright: 2012-04-09
  • Publisher: Princeton Univ Pr

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Summary

Most popular books about science, and even about mathematics, tiptoe around equations as if they were something to be hidden from the reader's tender eyes. Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics--the universal language of science--keep the masterpieces of the subject hidden behind a veil? The Universe in Zero Wordstells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society--from the elementary (1+1=2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E=mc2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called "a popular-science ace" by Booklistmagazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives. Illustrated in color throughout, the book tells the human and often-surprising stories behind the invention or discovery of the equations, from how a bad cigar changed the course of quantum mechanics to why whales (if they could communicate with us) would teach us a totally different concept of geometry. At the same time, the book shows why these equations have something timeless to say about the universe, and how they do it with an economy (zero words) that no other form of human expression can match. The Universe in Zero Wordsis the ultimate introduction and guide to equations that have changed the world.

Table of Contents

prefacep. 6
introduction: the abacist versus the algoristp. 10
equations of antiquityp. 16
Why we believe in arithmetic: the world's simplest equationp. 20
Resisting a new concept: the discovery of zerop. 26
The square of the hypotenuse: the Pythagorean theoremp. 30
The circle game: the discovery of ¿p. 40
From Zeno's paradoxes to the idea of infinityp. 46
A matter of leverage: laws of leversp. 52
equations in the age of explorationp. 56
The stammerer's secret: Cardano's formulap. 60
Order in the heavens: Kepler's laws of planetary motionp. 68
Writing for eternity: Fermat's Last Theoremp. 74
An unexplored continent: the fundamental theorem of calculusp. 80
Of apples, legends... and comets: Newton's lawsp. 90
The great explorer: Euler's theoremsp. 96
equations in a promethean agep. 104
The new algebra: Hamilton and quaternionsp. 108
Two shooting stars: group theoryp. 114
The geometry of whales and ants: non-Euclidean geometryp. 122
In primes we trust: the prime number theoremp. 128
The idea of spectra: Fourier seriesp. 134
A god's-eye view of light: Maxwell's equationsp. 142
equations in our own timep. 150
The photoelectric effect: quanta and relativityp. 154
From a bad cigar to Westminster Abbey: Dirac's formulap. 164
The empire-builder: the Chern-Gauss-Bonnet equationp. 174
A little bit infinite: the Continuum Hypothesisp. 182
Theories of chaos: Lorenz equationsp. 194
Taming the tiger: the Black-Scholes equationp. 204
conclusion: what of the future?p. 214
acknowledgmentsp. 218
bibliographyp. 219
indexp. 222ÿþ
Table of Contents provided by Ingram. All Rights Reserved.

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