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 3
... known as “Feynman point”, after the American Nobel prize winner Richard Feynman (1918–1988). He once claimed that if he had to recite the digits of T, he would name them accurately up to this point and only then say and so on. His words ...
... known as “Feynman point”, after the American Nobel prize winner Richard Feynman (1918–1988). He once claimed that if he had to recite the digits of T, he would name them accurately up to this point and only then say and so on. His words ...
Página 4
... known digits of T. Perhaps, but highly improbable. For example, the number which Y. Kanada has calculated does not even contain all the 20-digit numbers that are possible, which is 10", i.e. far more than the approximately 10" digits ...
... known digits of T. Perhaps, but highly improbable. For example, the number which Y. Kanada has calculated does not even contain all the 20-digit numbers that are possible, which is 10", i.e. far more than the approximately 10" digits ...
Página 5
... known to be irrational, as was demonstrated for the first time in 1766 by the Alsatian mathematician, Johann Heinrich Lambert (1728– 1777). An irrational number is one which cannot be represented as a ratio of two integers. For example ...
... known to be irrational, as was demonstrated for the first time in 1766 by the Alsatian mathematician, Johann Heinrich Lambert (1728– 1777). An irrational number is one which cannot be represented as a ratio of two integers. For example ...
Página 6
... known, all we know about the decimal sequence of T is trivial information such as the frequency and distribution of (short) blocks of numbers [11, p. 203]. The number T is thus one of the oldest subjects of research by mankind and ...
... known, all we know about the decimal sequence of T is trivial information such as the frequency and distribution of (short) blocks of numbers [11, p. 203]. The number T is thus one of the oldest subjects of research by mankind and ...
Página 7
... known in 414 BC that Aristophanes made use of it in his comedy “The Birds”. This is the problem of the squaring the circle, i.e. the challenge of finding a square which has exactly the same area as a given circle using a geometrical ...
... known in 414 BC that Aristophanes made use of it in his comedy “The Birds”. This is the problem of the squaring the circle, i.e. the challenge of finding a square which has exactly the same area as a given circle using a geometrical ...
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