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 background in mathematics, this biography of e brings out that number's central importance in mathematics and illuminates a golden era in the age of science.
Review:
... 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)
Table of contents:
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
Review:
... 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)
Table of contents:
Preface
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
Bibliography
Index
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