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
... world record by the Japanese Professor Kanada, who has now calculated T to 206.1 billion decimal places, and also the record achieved by Colin Percival, who in 1999 while still a teenager calculated the 40 trillionth binary digit of T ...
... world record by the Japanese Professor Kanada, who has now calculated T to 206.1 billion decimal places, and also the record achieved by Colin Percival, who in 1999 while still a teenager calculated the 40 trillionth binary digit of T ...
Página 2
... world records have generally been supercomputers which were specially developed for numbercrunching and cost millions of dollars. For example, Kanada achieved his latest record on a Hitachi SR8000 with 128 processors. Nevertheless, if ...
... world records have generally been supercomputers which were specially developed for numbercrunching and cost millions of dollars. For example, Kanada achieved his latest record on a Hitachi SR8000 with 128 processors. Nevertheless, if ...
Página 3
... world record, that this obvious question was finally answered. In fact that sequence does not occur until position ... world records shows on page 205. Number fanatics might perhaps search in T for “self-referential positions”, in which ...
... world record, that this obvious question was finally answered. In fact that sequence does not occur until position ... world records shows on page 205. Number fanatics might perhaps search in T for “self-referential positions”, in which ...
Página 12
... world record makes T the mathematical constant which has been calculated to the greatest number of decimal places ... world records can be found on the Internet at http://www.lacim. uquam. ca/pi/records.html. Not only are the first 206.1 ...
... world record makes T the mathematical constant which has been calculated to the greatest number of decimal places ... world records can be found on the Internet at http://www.lacim. uquam. ca/pi/records.html. Not only are the first 206.1 ...
Página 13
... world record of 100 decimal places: T 1 1 A T 4 arctan 5 arctan 239 (1.8) 4. The next sequence discovered by the Indian mathematician S. Ramanujan (1877–1920) in 1914 has the attraction that it converges extremely quickly. Every term in ...
... world record of 100 decimal places: T 1 1 A T 4 arctan 5 arctan 239 (1.8) 4. The next sequence discovered by the Indian mathematician S. Ramanujan (1877–1920) in 1914 has the attraction that it converges extremely quickly. Every term in ...
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