e: The Story of a Number : : The Story of a Number / / Eli Maor.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
• VerfasserIn: Maor, Eli,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2011]; ©1994
• Any de publicació: 2011
• Edició: Core Textbook
• Idioma: English
• Col·lecció: Princeton Science Library ; 72
• Descripció física: 1 online resource (248 p.) :; 6 halftones. 74 line illus.

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.

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? -- Appendixes -- 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