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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... Functions of the hfloat library. . . . . . . . . . . . . . . . . . . . . . . 248 A.4 Using hfloats in your own code. . . . . . . . . . . . . . . . . . . . . . 250 A.5 Computations with extreme precision . . . . . Contents XI.
... Functions of the hfloat library. . . . . . . . . . . . . . . . . . . . . . . 248 A.4 Using hfloats in your own code. . . . . . . . . . . . . . . . . . . . . . 250 A.5 Computations with extreme precision . . . . . Contents XI.
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... function. For it is the case that the function cosa. is positive at a = 0, but later on, for example when a = 2, it is negative. Since in between it runs continuously without any sudden changes, it must cross the x-axis at some point ...
... function. For it is the case that the function cosa. is positive at a = 0, but later on, for example when a = 2, it is negative. Since in between it runs continuously without any sudden changes, it must cross the x-axis at some point ...
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... function theory, complexity theory, the study of algorithms, statistics and other areas beside. Such a wide spectrum naturally exerts an exceptional fascination. For 4,000 years T has proved an inexhaustible source of new discoveries ...
... function theory, complexity theory, the study of algorithms, statistics and other areas beside. Such a wide spectrum naturally exerts an exceptional fascination. For 4,000 years T has proved an inexhaustible source of new discoveries ...
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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