"e": The Story of a Number: The Story of a Number

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number __e__. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of __e__ to mathematics and illuminates a golden era in the age of science. Contents Preface 1. John Napier, 1614 2 Recognition Computing with Logarithms 3 Financial Matters 4. To the Limit, If It Exists Some Curious Numbers Related to e 5. Forefathers of the Calculus 6. Prelude to Breakthrough Indivisibles at Work 7. Squaring the Hyperbola 8. The Birth of a New Science 9. The Great Controversy The Evolution of a Notation 10 e x : The Function That Equals Its Own Derivative The Parachutist Can Perceptions Be Quantified? 11 e θ Spira Mirabilis A Historic Meeting between J. S. Bach and Johann Bernoulli The Logarithmic Spiral in Art and Nature 12 (e x + e -x )/2: The Hanging Chain Remarkable Analogies Some Interesting Formulas Involving e 13 e ix . “The Most Famous of All Formulas” A Curious Episode in the History of e 14 e x+iy : The Imaginary Becomes Real A Most Remarkable Discovery 15. But What Kind of Number Is It? Appendixes Appendix 1. Some Additional Remarks on Napier’s Logarithms Appendix 2. The Existence of lim (1+1/n) n as n→∞ Appendix 3. A Heuristic Derivation of the Fundamental Theorem of Calculus Appendix 4. The Inverse Relation between lim (b h -1)/h = 1 and lim (1+h) 1/h as h→0 Appendix 5. An Alternative Definition of the Logarithmic Function Appendix 6. Two Properties of the Logarithmic Spiral Appendix 7. Interpretation of the Parameter Hyperbolic Functions Appendix 8. e to One Hundred Decimal Places Bibliography Index "The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest background in mathematics, this biography of e brings out that number's central importance in mathematics and illuminates a golden era in the age of science." -- Book cover Rarely in the history of science has an abstract mathematical idea been received more enthusiastically by the entire scientific community than the invention of logarithms.