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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... (base 10) . . . . . . . . . . . . 239 17.2 Digits 0 to 2,500 of T (base 10) . . . . . . . . . . . . . . . . . . . . . 240 17.3 Digits 2,501 to 5,000 of T (base 10) . . . . . . . . . . . . . . . . . . 241 17.4 Digits 0 to 2,500 of T (base ...
... (base 10) . . . . . . . . . . . . 239 17.2 Digits 0 to 2,500 of T (base 10) . . . . . . . . . . . . . . . . . . . . . 240 17.3 Digits 2,501 to 5,000 of T (base 10) . . . . . . . . . . . . . . . . . . 241 17.4 Digits 0 to 2,500 of T (base ...
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... base of natural logarithms” and whose value 2.71 . . . is fairly close to T, is also a transcendental number. Another reason could be that the two numbers are linked by a wonderful formula by Euler (1.10), to which we shall refer below ...
... base of natural logarithms” and whose value 2.71 . . . is fairly close to T, is also a transcendental number. Another reason could be that the two numbers are linked by a wonderful formula by Euler (1.10), to which we shall refer below ...
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... by Leonhard Euler dating from 1743. It combines five base quantities T, e, i, 0 and 1) and four basic operators (+, =, and exponentiation) into a single expression: e" + 1 = 0 (1.10) This formula has always 1. The State of Pi Art 13.
... by Leonhard Euler dating from 1743. It combines five base quantities T, e, i, 0 and 1) and four basic operators (+, =, and exponentiation) into a single expression: e" + 1 = 0 (1.10) This formula has always 1. The State of Pi Art 13.
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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