E: The Story of a Number - Brossura

Maor, Eli

Brossura

ISBN 10: 0691058547 ISBN 13: 9780691058542

Casa editrice: Princeton Univ Pr, 1998

Riassunto

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 numbere. 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.

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Recensione:

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

Contenuti:

	Preface
1	John Napier, 1614	3
2	Recognition	11
3	Financial Matters	23
4	To the Limit, If It Exists	28
5	Forefathers of the Calculus	40
6	Prelude to Breakthrough	49
7	Squaring the Hyperbola	58
8	The Birth of a New Science	70
9	The Great Controversy	83
10	e[superscript x]: The Function That Equals its Own Derivative	98
11	e[superscript theta]: Spira Mirabilis	114
12	(e[superscript x] + e[superscript -x])/2: The Hanging Chain	140
13	e[superscript ix]: "The Most Famous of All Formulas"	153
14	e[superscript x + iy]: The Imaginary Becomes Real	164
15	But What Kind of Number Is It?	183
	App. 1. Some Additional Remarks on Napier's Logarithms	195
	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 Calculus	200
	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	202
	App. 5. An Alternative Definition of the Logarithmic Function	203
	App. 6. Two Properties of the Logarithmic Spiral	205
	App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions	208
	App. 8. e to One Hundred Decimal Places	211
	Bibliography	213
	Index	217

Su questa edizione

• Editore: Princeton Univ Pr
• Data di pubblicazione: 1998
• ISBN 10: 0691058547
• ISBN 13: 9780691058542
• Rilegatura: Copertina flessibile
• Numero di pagine: 227