Dana Mackenzie
Princeton University Press | 2012 | 225 páginas | rar - pdf | 28,5 Mb
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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 Words tells 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" byBooklist magazine, 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 Words is the ultimate introduction and guide to equations that have changed the world.
contents
preface 6
introduction: the abacist versus the algorist 10
part one: equations of antiquity 16
1. Why we believe in arithmetic: the world’s simplest equation 20
2. Resisting a new concept: the discovery of zero 26
3. The square of the hypotenuse: the Pythagorean theorem 30
4. The circle game: the discovery of π 40
5. From Zeno’s paradoxes to the idea of infinity 46
6. A matter of leverage: laws of levers 52
part two: equations in the age of exploration 56
7. The stammerer’s secret: Cardano’s formula 60
8. Order in the heavens: Kepler’s laws of planetary motion 68
9. Writing for eternity: Fermat’s Last Theorem 74
10. An unexplored continent: the fundamental theorem of calculus 80
11. Of apples, legends . . . and comets: Newton’s laws 90
12. The great explorer: Euler’s theorems 96
part three: equations in a promethean age 104
13. The new algebra: Hamilton and quaternions 108
14. Two shooting stars: group theory 114
15. The geometry of whales and ants: non-Euclidean geometry 122
16. In primes we trust: the prime number theorem 128
17. The idea of spectra: Fourier series 134
18. A god’s-eye view of light: Maxwell’s equations 142
part four: equations in our own time 150
19. The photoelectric effect: quanta and relativity 154
20. From a bad cigar to Westminster Abbey: Dirac’s formula 164
21. The empire-builder: the Chern-Gauss-Bonnet equation 174
22. A little bit infinite: the Continuum Hypothesis 182
23. Theories of chaos: Lorenz equations 194
24. Taming the tiger: the Black-Scholes equation 204
conclusion: what of the future? 214
acknowledgments 218
bibliography 219
index
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