e: The Story of a Number

Front Cover
Princeton University Press, Oct 12, 2011 - 248 pages
3 Reviews

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.

 

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User Review  - James.Igoe - LibraryThing

Reading this book had me wondering about the mystical properties of numbers, whether there was some elemental truth I could discover. Overall, the book was an enjoyable and illuminating examination of e, and a solid retelling of e's importance in the development of trigonometry. Read full review

LibraryThing Review

User Review  - kcshankd - LibraryThing

I doubt this book appeals to readers with 'modest background in mathematics' as the cover promises. 'e' is the base of the natural logarithm. I vaguely recalled that e was the only number that was its ... Read full review

Contents

1 John Napier 1614
3
2 Recognition
11
Computing with Logarithms
18
3 Financial Matters
23
4 To the Limit If It Exists
28
Some Curious Numbers Relat ed to e
37
5 Forefathers of the Calculus
40
6 Prelude to Breakthrough
49
Remarkable Analogies
147
Some Interesting Formulas Involving e
151
The Most Famous of All Formulas
153
A Curious Episode in the History of e
162
The Imaginary Becomes Real
164
A Most Remarkable Discovery
183
15 But What Kind of Number Is It?
187
Appendixes
197

Indivisibles at Work
56
7 Squaring the Hyperbola
58
8 The Birth of a New Science
70
9 The Great Controversy
83
The Evolution of a Notation
95
The Function That Equals Its Own Derivative
98
The Parachutist
109
Can Perceptions Be Quantified ?
111
Spira Mirabilis
114
A Historic Meeting between J S Bach and Johann Bernoulli
129
The Logarithmic Spiral in Art and Nature
134
12 ex + ex2 The Hanging Chain
140
1 Some Additional Remarks on Napiers Logarithms
199
2 The Existence of lim 1 + 1nn as n
201
3 A Heuristic Derivation of the Fundamental Theorem of Calculus
204
4 The Inverse Relation between lim bh 1h 1 and lim 1 + h1h b as h0
206
5 An Alternative Definition of the Logarithmic Function
207
6 Two Properties of the Logarithmic Spiral
209
7 Interpretation of the Parameter in the Hyperbolic Functions
212
8 e to One Hundred Decimal Places
215
Bibliography
217
Index
221
Copyright

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About the author (2011)

Eli Maor is the author of Beautiful Geometry (with Eugen Jost), Venus in Transit, Trigonometric Delights, To Infinity and Beyond, and The Pythagorean Theorem: A 4,000-Year History (all Princeton).

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