"e": The Story of a Number

3.8 5
by Eli Maor
     
 

ISBN-10: 0691141347

ISBN-13: 9780691141343

Pub. Date: 01/19/2009

Publisher: Princeton University Press

The story of [pi] has been told many times, both in scholarly works and in popular books. But its close relative, the number e, has fared less well: despite the central role it plays in mathematics, its history has never before been written for a general audience. The present work fills this gap. Geared to the reader with only a modest background in mathematics, the…  See more details below

Overview

The story of [pi] has been told many times, both in scholarly works and in popular books. But its close relative, the number e, has fared less well: despite the central role it plays in mathematics, its history has never before been written for a general audience. The present work fills this gap. Geared to the reader with only a modest background in mathematics, the book describes the story of e from a human as well as a mathematical perspective. In a sense, it is the story of an entire period in the history of mathematics, from the early seventeenth to the late nineteenth century, with the invention of calculus at its center. Many of the players who took part in this story are here brought to life. Among them are John Napier, the eccentric religious activist who invented logarithms and - unknowingly - came within a hair's breadth of discovering e; William Oughtred, the inventor of the slide rule, who lived a frugal and unhealthful life and died at the age of 86, reportedly of joy when hearing of the restoration of King Charles II to the throne of England; Newton and his bitter priority dispute with Leibniz over the invention of the calculus, a conflict that impeded British mathematics for more than a century; and Jacob Bernoulli, who asked that a logarithmic spiral be engraved on his tombstone - but a linear spiral was engraved instead! The unifying theme throughout the book is the idea that a single number can tie together so many different aspects of mathematics - from the law of compound interest to the shape of a hanging chain, from the area under a hyperbola to Euler's famous formula e[superscript i[pi]] = -1, from the inner structure of a nautilus shell to Bach's equal-tempered scale and to the art of M. C. Escher. The book ends with an account of the discovery of transcendental numbers, an event that paved the way for Cantor's revolutionary ideas about infinity. No knowledge of calculus is assumed, and the few places where calculus is used are fully exp

Read More

Product Details

ISBN-13:
9780691141343
Publisher:
Princeton University Press
Publication date:
01/19/2009
Series:
Princeton Science Library Series
Pages:
248
Sales rank:
302,485
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

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >

"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