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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... arctan formula . . . . . . . . . . . . . . . . . . . . . . 69 5.2. Other arctan formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 10. 11. 12. Spigot Algorithms . . . . .
... arctan formula . . . . . . . . . . . . . . . . . . . . . . 69 5.2. Other arctan formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 10. 11. 12. Spigot Algorithms . . . . .
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... arctan formulae. The arctan formula used most frequently was first developed by John Machin (1680–1752), who used it in 1706 to generate what was then a world record of 100 decimal places: T 1 1 A T 4 arctan 5 arctan 239 (1.8) 4. The ...
... arctan formulae. The arctan formula used most frequently was first developed by John Machin (1680–1752), who used it in 1706 to generate what was then a world record of 100 decimal places: T 1 1 A T 4 arctan 5 arctan 239 (1.8) 4. The ...
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... arctan formulae method (see Chapter 5), dominated T calculations after that for more than 300 years until around 1980. The first extensive calculation of T on this basis produced exactly 100 digits in the year 1706 (using paper and ...
... arctan formulae method (see Chapter 5), dominated T calculations after that for more than 300 years until around 1980. The first extensive calculation of T on this basis produced exactly 100 digits in the year 1706 (using paper and ...
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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