Pi - UnleashedSpringer Science & Business Media, 6 dic 2012 - 270 páginas In the 4,000-year history of research into Pi, results have never been as prolific as present. This book describes, in easy-to-understand language, the latest and most fascinating findings of mathematicians and computer scientists in the field of Pi. Attention is focused on new methods of high-speed computation. |
Dentro del libro
Resultados 1-5 de 27
Página
... . . . . . . . . 170 13.3 Infinite expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 13.4 High-performance algorithms . . . . . . . . . . . . . . . . . . . . . . . 198 13.5 The hunt for single T digits ...
... . . . . . . . . 170 13.3 Infinite expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 13.4 High-performance algorithms . . . . . . . . . . . . . . . . . . . . . . . 198 13.5 The hunt for single T digits ...
Página 5
... infinite series of fractions in which all the numerators are equal to 1, T = 3 + 7+ —- 15+– 292 + – under which the fine structure of numbers becomes evident, has not revealed any regularities, although the simple continued fractions of ...
... infinite series of fractions in which all the numerators are equal to 1, T = 3 + 7+ —- 15+– 292 + – under which the fine structure of numbers becomes evident, has not revealed any regularities, although the simple continued fractions of ...
Página 7
... infinite. Simple questions - yet no one has solved them yet. With his proof of the transcendence of T, Lindemann also settled another problem which has preoccupied the brains of the best mathematicians and philosophers since the ancient ...
... infinite. Simple questions - yet no one has solved them yet. With his proof of the transcendence of T, Lindemann also settled another problem which has preoccupied the brains of the best mathematicians and philosophers since the ancient ...
Página 9
... infinite product comes to 3 × 3 × 5 × 5 X 7 x 7 x . . . . 4 1.2 2 x 4 x 4 x 6 x 6 x 8 x . . . . T (1.2) It is not difficult to see [123 that this Wallis product occurs in the formula for the calculation of p shown above, and in such a ...
... infinite product comes to 3 × 3 × 5 × 5 X 7 x 7 x . . . . 4 1.2 2 x 4 x 4 x 6 x 6 x 8 x . . . . T (1.2) It is not difficult to see [123 that this Wallis product occurs in the formula for the calculation of p shown above, and in such a ...
Página 12
... grandiose formulae for T has contributed to its fascination. Here is a selection of the available formulae, arranged in historical order: 1. François Viète (1540–1603) developed the first infinite product for 12 1. The State of Pi Art.
... grandiose formulae for T has contributed to its fascination. Here is a selection of the available formulae, arranged in historical order: 1. François Viète (1540–1603) developed the first infinite product for 12 1. The State of Pi Art.
Índice
7 | |
Approximations for T and Continued Fractions | 52 |
15 | 57 |
Arcus Tangens | 70 |
The Borweins and T | 114 |
Arithmetic 131 | 132 |
Computations with extreme precision | 250 |
Precision and radix | 251 |
Compiling running the Texamplecode | 253 |
Organisation of the files | 254 |
Distribution policy no warranty | 255 |
Bibliography 257 | 256 |
Index | 265 |
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Términos y frases comunes
accurate decimal places Adamchik AGM(a,b ak+1 approximation Archimedes Archimedes's arctan formulae arithmetic-geometric mean Arndt base BBP series Bellard Berlin Heidelberg 2001 billion decimal places billion digits binary modulo Borwein brothers calculation Chudnovsky brothers Cited Complex converge correct decimal places decimal digits denominator derived discovered discovery example expression fact fast Fourier transform FFT multiplication formula 7.1 function Gauss AGM algorithm geometric Golden ratio hexadecimal hexadecimal point hfloat infinite Initialise integer Internet iteration Kanada Karatsuba known Leibniz Leibniz series lemniscate length Leonhard Euler math mathematician method modular equations obtained occur operations perform perimeter Peter Borwein Plouffe polygons precision procedure produces proof provisional digit quadratic radix Ramanujan random numbers ratio representation result Schönhage sequence series term sides Simon Plouffe simple continued fraction spigot algorithm Springer-Verlag Berlin Heidelberg square root summand theorem tion Unleashed variables Viète world record Yasumasa Kanada zero