Preface1John Napier, 161432Recognition113Financial Matters234To the Limit, If It Exists285Forefathers of the Calculus406Prelude to Breakthrough497Squaring the Hyperbola588The Birth of a New Science709The Great Controversy8310e[superscript x]: The Function That Equals its Own Derivative9811e[superscript theta]: Spira Mirabilis11412(e[superscript x] + e[superscript -x])/2: The Hanging Chain14013e[superscript ix]: "The Most Famous of All Formulas"15314e[superscript x + iy]: The Imaginary Becomes Real16415But What Kind of Number Is It?183App. 1. Some Additional Remarks on Napier's Logarithms195App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches] [infinity]197App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus200App. 4. The Inverse Relation between lim (b[superscript h] - 1)/h = 1 and lim (1 + h)[superscript 1/h] = b as h [approaches] 0202App. 5. An Alternative Definition of the Logarithmic Function203App. 6. Two Properties of the Logarithmic Spiral205App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions208App. 8. e to One Hundred Decimal Places211Bibliography213Index217
Eli Maor is the author of "Venus in Transit", "Trigonometric Delights", "To Infinity and Beyond", and "The Pythagorean Theorem: A 4,000-Year History" (all Princeton). He teaches the history of mathematics at Loyola University in Chicago and at the Graham School of General Education at the University of Chicago.
Everyone whose mathematical education has gone beyond elementary school is familiar with the number known as pi. Far fewer have been introduced to e, a number that is of equal importance in theoretical mathematics. Maor (mathematics, Northeastern Illinois Univ.) tries to fill this gap with this excellent book. He traces the history of mathematics from the 16th century to the present through the intriguing properties of this number. Maor says that his book is aimed at the reader with a ``modest'' mathematical background. Be warned that his definition of modest may not be yours. The text introduces and discusses logarithms, limits, calculus, differential equations, and even the theory of functions of complex variables. Not easy stuff! Nevertheless, the writing is clear and the material fascinating. Highly recommended.-- Harold D. Shane, Baruch Coll., CUNY
Honorable Mention for the 1994 Award for Best Professional/Scholarly Book in Mathematics, Association of American Publishers "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 "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."--Choice "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."--EMS Newsletter