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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... examples, together with more detailed text on topics which had to be left out of the book due to space constraints. To help you get started with your own research on the Internet, we have also provided a collection of URLs. For the ...
... examples, together with more detailed text on topics which had to be left out of the book due to space constraints. To help you get started with your own research on the Internet, we have also provided a collection of URLs. For the ...
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... example-code . . . . . . . . . . . . 253 A.8 Structure of hfloat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 A.9 Organisation of the files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 A.10 ...
... example-code . . . . . . . . . . . . 253 A.8 Structure of hfloat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 A.9 Organisation of the files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 A.10 ...
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... examples of this. Thus, for example, a few years ago the above-mentioned Chudnovsky brothers calculated their 8 billion decimal digits of T in New York on a computer which they had built themselves from parts purchased in department ...
... examples of this. Thus, for example, a few years ago the above-mentioned Chudnovsky brothers calculated their 8 billion decimal digits of T in New York on a computer which they had built themselves from parts purchased in department ...
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... example, the author's birth dates are at positions 5,407,560 and 14,666,671). If I liked, I could print the position on my business cards, communicating vital information about what kind of person I am. On the Internet there is a game ...
... example, the author's birth dates are at positions 5,407,560 and 14,666,671). If I liked, I could print the position on my business cards, communicating vital information about what kind of person I am. On the Internet there is a game ...
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... example, in the 50th billion positions significantly more sixes occur than in the 60th billion. Anyone who succeeded in making such a pronouncement would certainly make the headlines. For up to now no one has found any sections within T ...
... example, in the 50th billion positions significantly more sixes occur than in the 60th billion. Anyone who succeeded in making such a pronouncement would certainly make the headlines. For up to now no one has found any sections within T ...
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