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

Eli Maor

Book

e: The Story of a Number

The Story of a Number

Eli Maor

Language: English

Published/Copyright: 1994

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This book is in the series

Volume 41 | Princeton Science Library

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 / Editor 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

"[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

"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."

"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."

"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

"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

"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

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

Topics

Mathematics History and Philosophy

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Frontmatter
I

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Contents
IX

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

Publishing information

Pages and Images/Illustrations in book

eBook published on:

October 12, 2011

eBook ISBN:

9781400832347

Edition:

Core Textbook

Pages and Images/Illustrations in book

Main content:

248

Other:

6 halftones. 74 line illus.

https://doi.org/10.1515/9781400832347

eBook ISBN: 9781400832347

Keywords for this book

Mathematics; Logarithm; Equation; Quantity; Mathematician; Summation; Hyperbola; Real number; Derivative; Parabola; Exponential function; Circumference; Rational number; Scientific notation; Geometry; Euler's formula; Notation; Irrational number; Trigonometric functions; Geometric progression; Coefficient; Addition; Differential equation; Square root; Variable (mathematics); Series (mathematics); Special case; Hyperbolic function; Natural number; Antiderivative; Significant figures; Unit circle; Method of exhaustion; Fluxion; Tangent; Integer; Algebraic equation; Limit (mathematics); Complex number; Line segment; Coordinate system; Theorem; Accuracy and precision; Natural logarithm; Exponentiation; Infinite product; Number theory; Result; Leonhard Euler; Proportionality (mathematics); Power series; Pure mathematics; Diameter; Conic section; Inverse function; Differential calculus; Sign (mathematics); Leibniz's notation; Rectangle; Catenary; Interest rate; Logarithmic spiral; Compound interest; Infinitesimal; Cartesian coordinate system; Trigonometry; Scientist; Prime number; Polynomial; Elementary algebra

Audience(s) for this book

General/trade;

e: The Story of a Number

Overview

About this book

Author / Editor information

Reviews

Topics

Table of contents

Frontmatter

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 ex: The Function That Equals Its Own Derivative

The Parachutist

Can Perceptions Be Quantified?

11 eθ Spira Mirabilis

A Historic Meeting between J. S. Bach and Johann Bernoulli

The Logarithmic Spiral in Art and Nature

12 (ex + e-x)/2: The Hanging Chain

Remarkable Analogies

Some Interesting Formulas Involving e

13 eix. “The Most Famous of All Formulas”

A Curious Episode in the History of e

14 ex+iy: The Imaginary Becomes Real

A Most Remarkable Discovery

15. But What Kind of Number Is It?

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 (bh-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

Bibliographic data

10 e^x: The Function That Equals Its Own Derivative

11 e^θ Spira Mirabilis

12 (e^x + e^-x)/2: The Hanging Chain

13 e^ix. “The Most Famous of All Formulas”

14 e^x+iy: The Imaginary Becomes Real

Appendix 2. The Existence of lim (1+1/n)ⁿ as n→∞

Appendix 4. The Inverse Relation between lim (b^h-1)/h = 1 and lim (1+h)^1/h as h→0