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

Eli Maor

Published by Princeton University Press 1994

e: The Story of a Number

The Story of a Number

Eli Maor

Volume 41 in the series Princeton Science Library

https://doi.org/10.1515/9781400832347

Overview
Contents

About this book

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.

Author information

Eli Maor is the author of Beautiful Geometry (with Eugen Jost), Venus in Transit, Trigonometric Delights, To Infinity and Beyond, and The Pythagorean Theorem: A 4,000-Year History (all Princeton).

Reviews

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.

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

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

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.

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

[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, Nature

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	IX
Preface Requires Authentication Unlicensed Licensed Download PDF	XI
1. John Napier, 1614 Requires Authentication Unlicensed Licensed Download PDF	1
2 Recognition Requires Authentication Unlicensed Licensed Download PDF	11
Computing with Logarithms Requires Authentication Unlicensed Licensed Download PDF	18
3 Financial Matters Requires Authentication Unlicensed Licensed Download PDF	23
4. To the Limit, If It Exists Requires Authentication Unlicensed Licensed Download PDF	28
Some Curious Numbers Related to e Requires Authentication Unlicensed Licensed Download PDF	37
5. Forefathers of the Calculus Requires Authentication Unlicensed Licensed Download PDF	40
6. Prelude to Breakthrough Requires Authentication Unlicensed Licensed Download PDF	49
Indivisibles at Work Requires Authentication Unlicensed Licensed Download PDF	56
7. Squaring the Hyperbola Requires Authentication Unlicensed Licensed Download PDF	58
8. The Birth of a New Science Requires Authentication Unlicensed Licensed Download PDF	70
9. The Great Controversy Requires Authentication Unlicensed Licensed Download PDF	83
The Evolution of a Notation Requires Authentication Unlicensed Licensed Download PDF	95
10 e^x: The Function That Equals Its Own Derivative Requires Authentication Unlicensed Licensed Download PDF	98
The Parachutist Requires Authentication Unlicensed Licensed Download PDF	109
Can Perceptions Be Quantified? Requires Authentication Unlicensed Licensed Download PDF	111
11 e^θ Spira Mirabilis Requires Authentication Unlicensed Licensed Download PDF	114
A Historic Meeting between J. S. Bach and Johann Bernoulli Requires Authentication Unlicensed Licensed Download PDF	129
The Logarithmic Spiral in Art and Nature Requires Authentication Unlicensed Licensed Download PDF	134
12 (e^x + e^-x)/2: The Hanging Chain Requires Authentication Unlicensed Licensed Download PDF	140
Remarkable Analogies Requires Authentication Unlicensed Licensed Download PDF	147
Some Interesting Formulas Involving e Requires Authentication Unlicensed Licensed Download PDF	151
13 e^ix. “The Most Famous of All Formulas” Requires Authentication Unlicensed Licensed Download PDF	153
A Curious Episode in the History of e Requires Authentication Unlicensed Licensed Download PDF	162
14 e^x+iy: The Imaginary Becomes Real Requires Authentication Unlicensed Licensed Download PDF	164
A Most Remarkable Discovery Requires Authentication Unlicensed Licensed Download PDF	183
15. But What Kind of Number Is It? Requires Authentication Unlicensed Licensed Download PDF	187
Appendixes
Appendix 1. Some Additional Remarks on Napier’s Logarithms Requires Authentication Unlicensed Licensed Download PDF	199
Appendix 2. The Existence of lim (1+1/n)ⁿ as n→∞ Requires Authentication Unlicensed Licensed Download PDF	201
Appendix 3. A Heuristic Derivation of the Fundamental Theorem of Calculus Requires Authentication Unlicensed Licensed Download PDF	204
Appendix 4. The Inverse Relation between lim (b^h-1)/h = 1 and lim (1+h)^1/h as h→0 Requires Authentication Unlicensed Licensed Download PDF	206
Appendix 5. An Alternative Definition of the Logarithmic Function Requires Authentication Unlicensed Licensed Download PDF	207
Appendix 6. Two Properties of the Logarithmic Spiral Requires Authentication Unlicensed Licensed Download PDF	209
Appendix 7. Interpretation of the Parameter Hyperbolic Functions Requires Authentication Unlicensed Licensed Download PDF	212
Appendix 8. e to One Hundred Decimal Places Requires Authentication Unlicensed Licensed Download PDF	215
Bibliography Requires Authentication Unlicensed Licensed Download PDF	217
Index Requires Authentication Unlicensed Licensed Download PDF	221

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