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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... 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, 400 million decimal places of T and several ...
... 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, 400 million decimal places of T and several ...
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... decimal places. In this book you will discover why anyone should be interested in achieving world records with such bizarre calculations, which are long enough to fill up thousands of phone directories, and you will also find many other ...
... decimal places. In this book you will discover why anyone should be interested in achieving world records with such bizarre calculations, which are long enough to fill up thousands of phone directories, and you will also find many other ...
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Jörg Arndt, Christoph Haenel. J. Arndt et al., Pi - Unleashed © Springer-Verlag Berlin Heidelberg 2001 decimal place was reached. Since 1997 and from 51 billion.
Jörg Arndt, Christoph Haenel. J. Arndt et al., Pi - Unleashed © Springer-Verlag Berlin Heidelberg 2001 decimal place was reached. Since 1997 and from 51 billion.
Página 2
... decimal digits of T in New York on a computer which they had built themselves from parts purchased in department stores (92). One might expect Kanada to record his T calculations in compressed form” on around 150 CDs and to offer them ...
... decimal digits of T in New York on a computer which they had built themselves from parts purchased in department stores (92). One might expect Kanada to record his T calculations in compressed form” on around 150 CDs and to offer them ...
Página 3
... point”, after the American Nobel prize winner Richard Feynman (1918–1988). He once claimed that if he had to recite the ... places after that. * It is customary to count digit positions from 0, beginning with the 3 in front of the decimal ...
... point”, after the American Nobel prize winner Richard Feynman (1918–1988). He once claimed that if he had to recite the ... places after that. * It is customary to count digit positions from 0, beginning with the 3 in front of the decimal ...
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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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