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. |
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Página 2
... perform T calculations which are still competitive. In the history of the world records there have been several examples of this. Thus, for example, a few years ago the above-mentioned Chudnovsky brothers calculated their 8 billion ...
... perform T calculations which are still competitive. In the history of the world records there have been several examples of this. Thus, for example, a few years ago the above-mentioned Chudnovsky brothers calculated their 8 billion ...
Página 11
... perform his T calculations. The Borweins and a number of other researchers also make their publications available for reading and downloading. There are a number of cheerful T clubs on the Internet. It is possible to become a formal ...
... perform his T calculations. The Borweins and a number of other researchers also make their publications available for reading and downloading. There are a number of cheerful T clubs on the Internet. It is possible to become a formal ...
Página 12
... performed by Kanada. These are followed (as of October 1999) by e = 2.71828.18284... (as mentioned above, either 1 billion or 200 million), Riemann's number (3) = XX: 1: = 1.2020569031... (128 million) and ln(2) = 0.6931471805. . . (108 ...
... performed by Kanada. These are followed (as of October 1999) by e = 2.71828.18284... (as mentioned above, either 1 billion or 200 million), Riemann's number (3) = XX: 1: = 1.2020569031... (128 million) and ln(2) = 0.6931471805. . . (108 ...
Página 13
... performed using arctan formulae. The arctan formula used most frequently was first developed by John Machin (1680–1752), who used it in 1706 to generate what was then a world record of 100 decimal places: T 1 1 A T 4 arctan 5 arctan 239 ...
... performed using arctan formulae. The arctan formula used most frequently was first developed by John Machin (1680–1752), who used it in 1706 to generate what was then a world record of 100 decimal places: T 1 1 A T 4 arctan 5 arctan 239 ...
Página 16
... perform multiplication operations no longer rises quadratically as the number of factors is increased, as had been the case in what was previously virtually the only multiplication “school”, but more or less linearly. In Chapter 11 we ...
... perform multiplication operations no longer rises quadratically as the number of factors is increased, as had been the case in what was previously virtually the only multiplication “school”, but more or less linearly. In Chapter 11 we ...
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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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