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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... calculations, is explained in detail with appropriate examples of code. The historical section has been completely reworked and considerably enlarged. We have also expanded the (platform-independent) CD-ROM to include, in particular ...
... calculations, is explained in detail with appropriate examples of code. The historical section has been completely reworked and considerably enlarged. We have also expanded the (platform-independent) CD-ROM to include, in particular ...
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... calculations, which are long enough to fill up thousands of phone directories, and you will also find many other interesting things about this number. The methods which are used for these high-precision calculations reflect developments ...
... calculations, which are long enough to fill up thousands of phone directories, and you will also find many other interesting things about this number. The methods which are used for these high-precision calculations reflect developments ...
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... calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 12.1 AT quiz . . . . . . . . . . . . . . . . . . . .
... calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 12.1 AT quiz . . . . . . . . . . . . . . . . . . . .
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... Calculations on the Internet . . . . . . . . . 215 15.1 The binsplit algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 15.2 The T project on the Internet . . . . . . . . . . . . . . . . . . . . . . . 219 T Formula ...
... Calculations on the Internet . . . . . . . . . 215 15.1 The binsplit algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 15.2 The T project on the Internet . . . . . . . . . . . . . . . . . . . . . . . 219 T Formula ...
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... calculations which are still competitive. In the history of the world records there have been several examples of this. Thus, for example, a few years ago the above-mentioned Chudnovsky brothers calculated their 8 billion decimal digits ...
... calculations which are still competitive. In the history of the world records there have been several examples of this. Thus, for example, a few years ago the above-mentioned Chudnovsky brothers calculated their 8 billion decimal digits ...
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