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 12
... hexadecimal representation, an A. This and other such astonishing findings resulted from the use of a new approach to the calculation of T which was discovered quite by surprise in 1995. This subject is discussed in Chapter 10. Whereas ...
... hexadecimal representation, an A. This and other such astonishing findings resulted from the use of a new approach to the calculation of T which was discovered quite by surprise in 1995. This subject is discussed in Chapter 10. Whereas ...
Página 19
... hexadecimal digits in T to be calculated without having to calculate all the digits which come before. The basis for this is the following new formula: £ 1 4 2 1 1. "-21. (#. 8n +4 8n +5. **). (1.12) The inventors of this formula (David ...
... hexadecimal digits in T to be calculated without having to calculate all the digits which come before. The basis for this is the following new formula: £ 1 4 2 1 1. "-21. (#. 8n +4 8n +5. **). (1.12) The inventors of this formula (David ...
Página 20
... hexadecimal digit of T, which at the time was far off from discovery. The new idea seems to have electrified T researchers all around the world. Since then they have found more formulae of the same type as the BBP series and even an ...
... hexadecimal digit of T, which at the time was far off from discovery. The new idea seems to have electrified T researchers all around the world. Since then they have found more formulae of the same type as the BBP series and even an ...
Página 32
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Página 52
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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