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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... Chudnovsky brothers calculated their 8 billion decimal digits of T in New York on a computer which they had built themselves from parts purchased in department stores (92). One might expect Kanada to record his T calculations in ...
... Chudnovsky brothers calculated their 8 billion decimal digits of T in New York on a computer which they had built themselves from parts purchased in department stores (92). One might expect Kanada to record his T calculations in ...
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... Chudnovsky brothers are said to have calculated e to 1 billion digits, but this has not been officially confirmed.) Due to this disparity it is assumed that e is in principle more difficult to calculate than T, but this has not been ...
... Chudnovsky brothers are said to have calculated e to 1 billion digits, but this has not been officially confirmed.) Due to this disparity it is assumed that e is in principle more difficult to calculate than T, but this has not been ...
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... Chudnovsky brothers (8.7), who used it in 1989 to calculate 15 digits per term and thus to attain what was then a world record of 1 billion digits. Other T algorithms which operate in an entirely different fashion 16 1. The State of Pi Art.
... Chudnovsky brothers (8.7), who used it in 1989 to calculate 15 digits per term and thus to attain what was then a world record of 1 billion digits. Other T algorithms which operate in an entirely different fashion 16 1. The State of Pi Art.
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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