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
... facts of scientific interest but also some examples of both the curious and the bizarre. The following persons provided extremely useful comments and suggestions as we were writing the book: Dieter Beule, Lothar Krüger, Heinz Pöhlmann ...
... facts of scientific interest but also some examples of both the curious and the bizarre. The following persons provided extremely useful comments and suggestions as we were writing the book: Dieter Beule, Lothar Krüger, Heinz Pöhlmann ...
Página 2
... fact already the case today. And even a sophisticated T program will always be shorter than the number of digits to which it can calculate. What is the point of having such a long representation of T'? One obvious task is to search ...
... fact already the case today. And even a sophisticated T program will always be shorter than the number of digits to which it can calculate. What is the point of having such a long representation of T'? One obvious task is to search ...
Página 3
... fact that sequence does not occur until position 17,387,594,880, i.e. long past the 6.4 billionth digit, which was previously the furthest that was known. But, if this special sequence does not occur until that late, another special ...
... fact that sequence does not occur until position 17,387,594,880, i.e. long past the 6.4 billionth digit, which was previously the furthest that was known. But, if this special sequence does not occur until that late, another special ...
Página 4
... fact we have little more than 10". Even worse, it simply is not possible for theoretical reasons to calculate T to so many digits, for the universe consists only of 10" elementary particles, and even if one were to turn the entire ...
... fact we have little more than 10". Even worse, it simply is not possible for theoretical reasons to calculate T to so many digits, for the universe consists only of 10" elementary particles, and even if one were to turn the entire ...
Página 8
... these relationships involve the same ratio, T. This fact is not readily understood. The picture below is perhaps the simplest way of examining the concept: -> WWWWWW* circumference In the picture on the left, a 8 1. The State of Pi Art.
... these relationships involve the same ratio, T. This fact is not readily understood. The picture below is perhaps the simplest way of examining the concept: -> WWWWWW* circumference In the picture on the left, a 8 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