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 15
... Archimedes of Syracuse. Whereas up to then only experimental methods had been used, he was the first person to develop a systematic procedure for arriving at limits for T. He calculated the circumferences of regular polygons which he ...
... Archimedes of Syracuse. Whereas up to then only experimental methods had been used, he was the first person to develop a systematic procedure for arriving at limits for T. He calculated the circumferences of regular polygons which he ...
Página 16
... Archimedes and his polygon method determined the direction in which virtually all succeeding T mathematicians proceeded for nearly 2000 years. Over the centuries mathematicians increased the number of sides in the polygons used for the ...
... Archimedes and his polygon method determined the direction in which virtually all succeeding T mathematicians proceeded for nearly 2000 years. Over the centuries mathematicians increased the number of sides in the polygons used for the ...
Página 55
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Página 64
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Página 172
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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