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Euler's pioneering equation : the most beautiful theorem in mathematics /
In just seven symbols, with profound and beautiful simplicity, Euler's Equation connects five of the most important numbers in mathematics. Robin Wilson explores each number in turn, then brings them together to consider the power of the equation as a whole.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford, United Kingdom :
Oxford University Press,
2018.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Euler's Pioneering Equation: The most beautiful theorem in mathematics; Copyright; Preface; Contents; INTRODUCTION; The most beautiful theorem in mathematics; Euler, his equation, and his identity; Chapter 1: 1; The counting numbers; Number systems; Decimal numbers; Binary numbers; Roman numbers; Egyptian numbers; Mesopotamian numbers; Greek numbers; Chinese numbers; Mayan numbers; The Hinduâ#x80;#x93;Arabic numbers; Number names; Chapter 2: 0; The nothingness number; Much ado about nothing; Calculating with zero and negative numbers; â#x80;#x98;Thou shalt not divide by zeroâ#x80;#x99.
- From integers to real numbersFractions; Irrational numbers; Real numbers; Algebraic and transcendental numbers; Chapter 3: Ï#x80;; The circle number; Why Ï#x80;?; Early values; Using polygons; Radian measure; Infinite expressions; ViÃẗeâ#x80;#x99;s infinite product; Wallisâ#x80;#x99;s infinite product; Continued fractions; Arctan formulas; A miscellany of results; Some results of Euler; Probabilistic results; Buffonâ#x80;#x99;s needle experiment; Gaussâ#x80;#x99;s circle problem; Ï#x80; is irrational; Legislating for Ï#x80;; Some weird results; Enter the computer; Why bother?; Measuring the Earth; Chapter 4: e; The exponential number.
- Polynomial and exponential growthComparing types of growth; Introducing logarithms; Logarithms to base 2; The logarithms of Napier and Briggs; Enter the calculus; A problem of interest; Properties of e; e as a limit; e as an infinite series; The multiplication rule; The slope of the graph of y = e x; Exponentials and logarithms are inverse functions; e is irrational; Napierâ#x80;#x99;s definition of the logarithm; Hanging chains and derangements; Hanging chains; Derangements; Exponential growth and decay; Population growth; Cooling of a cup of tea; The half-life of radium; Chapter 5: i.
- The imaginary numberDifferent types of numbers; Solving equations; The fundamental theorem of algebra; The origins of i; Picturing complex numbers; Constructing square roots; The complex plane; Argand and Gauss; Generalizing complex numbers; Hamiltonâ#x80;#x99;s quaternions; Octonions; Chapter 6: eiÏ#x80; + 1 = 0; Eulerâ#x80;#x99;s equation; Two near misses; Johann Bernoulli; Roger Cotes; Eulerâ#x80;#x99;s identity; Some consequences; Eulerâ#x80;#x99;s equation; De Moivreâ#x80;#x99;s theorem; Multiplying complex numbers; Relating the trigonometric and hyperbolic functions; Roots of 1; The golden ratio; e and Ï#x80; are transcendental.
- What are ln i, ii, and iâ#x88;#x9A;iWhat is ln i?; What are ii and iâ#x88;#x9A;i?; Who discovered Eulerâ#x80;#x99;s equation?; FURTHER READING; Euler; The most beautiful equation; Introduction; Number systems; Ï#x80;, e, and i; Eulerâ#x80;#x99;s equation; IMAGE CREDITS; PUBLISHERâ#x80;#x99;S ACKNOWLEDGEMENTS; INDEX.