TABLE OF 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 222 Return to Book Description File created: 4/27/2015 |