'e:' the Story of a Number (ebook)

Argumento de 'e:' the Story of a Number (ebook)

"Maor attempts to give the irrational number e its rightful standing alongside pi as a fundamental constant in science and nature; he succeeds very well.... Maor writes so that both mathematical newcomers and long-time professionals alike can thoroughly enjoy his book, learn something new, and witness the ubiquity of mathematical ideas in Western culture."--Choice

"Maor has succeeded in writing a short, readable mathematical story. He has interspersed a variety of anecdotes, excursions, and essays to lighten the flow.... [The book] is like the voyages of Columbus as told by the first mate."--Peter Borwein, Science

Honorable Mention for the 1994 Award for Best Professional/Scholarly Book in Mathematics, Association of American Publishers

"This is a gently paced, elegantly composed book, and it will bring its readers much pleasure. . . . Maor has written an excellent book that should be in every public and school library."--Ian Stewart, New Scientist

"It can be recommended to readers who want to learn about mathematics and its history, who want to be inspired and who want to understand important mathematical ideas more deeply."--EMS Newsletter

"[A] very interesting story about the history of e, logarithms, and related matters, especially the history of calculus. . . . [A] useful complement to a course in calculus and analysis, shedding light on some fundamental topics."--Mehdi Hassani, MAA Reviews

"Maor wonderfully tells the story of e. The chronological history allows excursions into the lives of people involved with the development of this fascinating number. Maor hangs his story on a string of people stretching from Archimedes to David Hilbert. And by presenting mathematics in terms of the humans who produced it, he places the subject where it belongs--squarely in the centre of the humanities."--Jerry P. King, Nature0Preface 1 John Napier, 1614 3 2 Recognition 11 3 Financial Matters 23 4 To the Limit, If It Exists 28 5 Forefathers of the Calculus 40 6 Prelude to Breakthrough 49 7 Squaring the Hyperbola 58 8 The Birth of a New Science 70 9 The Great Controversy 83 10 e[superscript x]: The Function That Equals its Own Derivative 98 11 e[superscript theta]: Spira Mirabilis 114 12 (e[superscript x] + e[superscript -x])/2: The Hanging Chain 140 13 e[superscript ix]: "The Most Famous of All Formulas" 153 14 e[superscript x + iy]: The Imaginary Becomes Real 164 15 But What Kind of Number Is It? 183 App. 1. Some Additional Remarks on Napier's Logarithms 195 App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches] [infinity] 197 App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus 200 App. 4. The Inverse Relation between lim (b[superscript h] - 1)/h = 1 and lim (1 + h)[superscript 1/h] = b as h [approaches] 0 202 App. 5. An Alternative Definition of the Logarithmic Function 203 App. 6. Two Properties of the Logarithmic Spiral 205 App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions 208 App. 8. e to One Hundred Decimal Places 211 Bibliography 213 Index 217