"e": The Story of a Number

3.8 5
by Eli Maor
     
 

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ISBN-10: 0691141347

ISBN-13: 9780691141343

Pub. Date: 01/19/2009

Publisher: Princeton University Press

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

Overview

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."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"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"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

Product Details

ISBN-13:
9780691141343
Publisher:
Princeton University Press
Publication date:
01/19/2009
Series:
Princeton Science Library Series
Pages:
248
Product dimensions:
6.10(w) x 9.20(h) x 0.70(d)

Table of Contents

Preface
1John Napier, 16143
2Recognition11
3Financial Matters23
4To the Limit, If It Exists28
5Forefathers of the Calculus40
6Prelude to Breakthrough49
7Squaring the Hyperbola58
8The Birth of a New Science70
9The Great Controversy83
10e[superscript x]: The Function That Equals its Own Derivative98
11e[superscript theta]: Spira Mirabilis114
12(e[superscript x] + e[superscript -x])/2: The Hanging Chain140
13e[superscript ix]: "The Most Famous of All Formulas"153
14e[superscript x + iy]: The Imaginary Becomes Real164
15But What Kind of Number Is It?183
App. 1. Some Additional Remarks on Napier's Logarithms195
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 Calculus200
App. 4. The Inverse Relation between lim (b[superscript h] - 1)/h = 1 and lim (1 + h)[superscript 1/h] = b as h [approaches] 0202
App. 5. An Alternative Definition of the Logarithmic Function203
App. 6. Two Properties of the Logarithmic Spiral205
App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions208
App. 8. e to One Hundred Decimal Places211
Bibliography213
Index217

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"e": The Story of a Number 3.8 out of 5 based on 0 ratings. 5 reviews.
AnnieBM More than 1 year ago
This book is a bit challenging for the not so mathematically inclined but still an excellent history with meaningful portrayals of the historical figures, mostly mathematicians involved in the story. Maor does an excellent job of leading the reader through derivations and problem solving. He spices the story with great quotes and biographic details. I read this book because I wanted to know more about e -- we use it in several important equations in population ecology. I was greatly rewarded by not only learning more about e, but also the place of mathematics in society, intellectual history, and the personalities and their relationships, both personal and historical. Highly recommended for the inellectually curious.
Anonymous More than 1 year ago
The number e is a part of all of our lives in ways most of us never imagined. This is a very readable, non-technical book with a lot of amazing insights. Well written and engaging. If you, or your high school/college age children, have any interest in math professionally or as a hobby you really ought to read this book.
Anonymous More than 1 year ago
Anonymous More than 1 year ago
This Is Review body Test; Edited text searchWord = e Thu Oct 22 2009 20:55:30 GMT-0400 (Eastern Daylight Time) 3
Anonymous More than 1 year ago
This Is Review body Test; Edited text Mon Sep 21 2009 11:18:43 GMT-0400 (Eastern Daylight Time) 1