Description 
xiv, 227 pages : illustrations ; 25 cm 
Contents 
1. John Napier, 1614  2. Recognition  3. Financial Matters  4. To the Limit, If It Exists  5. Forefathers of the Calculus  6. Prelude to Breakthrough  7. Squaring the Hyperbola  8. The Birth of a New Science  9. The Great Controversy  10. e[superscript x]: The Function That Equals its Own Derivative  11. e[superscript theta]: Spira Mirabilis  12. (e[superscript x] + e[superscript x])/2: The Hanging Chain  13. e[superscript ix]: "The Most Famous of All Formulas"  14. e[superscript x + iy]: The Imaginary Becomes Real  15. But What Kind of Number Is It?  App. 1. Some Additional Remarks on Napier's Logarithms  App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches] [infinity]  App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus  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 

App. 5. An Alternative Definition of the Logarithmic Function  App. 6. Two Properties of the Logarithmic Spiral  App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions  App. 8. e to One Hundred Decimal Places 
Summary 
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 equaltempered 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 explained 
Analysis 
Number theory 

Number theory 
Bibliography 
Includes bibliographical references (pages [217]219) and index 
Subject 
e (The number)


Logarithms  History.


Mathematics.


Transcendental numbers.


e (The number)

LC no. 
93039003 
ISBN 
0691058547 
