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 3
... 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 sequence, consisting of 10 ...
... 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 sequence, consisting of 10 ...
Página 4
... occur in Kanada's number. Still less does it contain all the 21-digit numbers, let alone all the numbers of DNA or Bible length. This makes it unlikely that the Bible, with its estimated 10" digits, occurs in the first “few” digits of T ...
... occur in Kanada's number. Still less does it contain all the 21-digit numbers, let alone all the numbers of DNA or Bible length. This makes it unlikely that the Bible, with its estimated 10" digits, occurs in the first “few” digits of T ...
Página 5
Jörg Arndt, Christoph Haenel. numbers or blocks of numbers of the same length occur more often or less often than others, so that, for example, in the 50th billion positions significantly more sixes occur than in the 60th billion. Anyone ...
Jörg Arndt, Christoph Haenel. numbers or blocks of numbers of the same length occur more often or less often than others, so that, for example, in the 50th billion positions significantly more sixes occur than in the 60th billion. Anyone ...
Página 7
... occur according to Lindemann's proof. Hence, it is not possible to square the circle with a geometric construction using only compass and ruler. (On the other hand it is possible if the constraining conditions are varied. For example ...
... occur according to Lindemann's proof. Hence, it is not possible to square the circle with a geometric construction using only compass and ruler. (On the other hand it is possible if the constraining conditions are varied. For example ...
Página 9
... . . . . T (1.2) It is not difficult to see [123 that this Wallis product occurs in the formula for the calculation of p shown above, and in such a manner that p = 1/VT. n. (1.3) which, for example produces a. 1. The State of Pi Art 9.
... . . . . T (1.2) It is not difficult to see [123 that this Wallis product occurs in the formula for the calculation of p shown above, and in such a manner that p = 1/VT. n. (1.3) which, for example produces a. 1. The State of Pi Art 9.
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