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
... . . . . . . . . 78 6.2 Sequence of operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.3 A faster variant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.4 Spigot algorithm for e ...
... . . . . . . . . 78 6.2 Sequence of operations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.3 A faster variant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.4 Spigot algorithm for e ...
Página 2
... sequences of the same digits. For the first few thousand digits, which are shown on page 240ff of this book, it is probably still feasible to do this without a computer. Above that limit, however, one will probably need a search program ...
... sequences of the same digits. For the first few thousand digits, which are shown on page 240ff of this book, it is probably still feasible to do this without a computer. Above that limit, however, one will probably need a search program ...
Página 3
... sequence 0123456789 first appear in T'? It was only in 1997, at the time of the last but one world record, that this obvious question was finally answered. In fact that sequence does not occur until position 17,387,594,880, i.e. long ...
... sequence 0123456789 first appear in T'? It was only in 1997, at the time of the last but one world record, that this obvious question was finally answered. In fact that sequence does not occur until position 17,387,594,880, i.e. long ...
Página 6
... sequence of T is trivial information such as the frequency and distribution of (short) blocks of numbers [11, p. 203]. The number T is thus one of the oldest subjects of research by mankind and possibly the one topic within mathematics ...
... sequence of T is trivial information such as the frequency and distribution of (short) blocks of numbers [11, p. 203]. The number T is thus one of the oldest subjects of research by mankind and possibly the one topic within mathematics ...
Página 7
... sequences of two prime numbers separated by 2 such as the sequence 3 and 5 or 10,007 and 10,009, is infinite. Simple questions - yet no one has solved them yet. With his proof of the transcendence of T, Lindemann also settled another ...
... sequences of two prime numbers separated by 2 such as the sequence 3 and 5 or 10,007 and 10,009, is infinite. Simple questions - yet no one has solved them yet. With his proof of the transcendence of T, Lindemann also settled another ...
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