"e": The Story of a NumberPrinceton University Press, 19 gen 2009 - 227 pagine 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. |
Sommario
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 |
| 217 | |
| 221 | |
Altre edizioni - Visualizza tutto
Parole e frasi comuni
algebraic angle antiderivative Archimedes Bach base Bernoulli catenary century coefficients complex numbers complex variable compute constant converges curve decimal defined denote derivative differential equation discovery distance dy/dx equal Euler Euler's formula example exponent exponential function expression Fermat's find the area Florian Cajori fluxions fractions func geometric progression given graph Greeks History of Mathematics hyperbola hyperbolic functions imaginary increase infinite series infinity integral calculus invention inverse irrational numbers Jakob Jakob Bernoulli Johann known Leibniz limit loga logarithmic spiral mathe mathematician method method of exhaustion method of fluxions Napier natural logarithm Newton notation NOTES AND SOURCES parabola Pascal's triangle polynomial primes problem proof published quantities rate of change ratio rational numbers real number rectangles result rules segment side sinh solution solve square symbol tangent line Theorem tion triangle x-axis z-plane