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 4
... side of that limit can be calculated. Anyone who wants to make a name for himself can examine the major issue of whether T is normal, or perhaps more accurately, whether T is not normal. If T were not normal, this would mean that ...
... side of that limit can be calculated. Anyone who wants to make a name for himself can examine the major issue of whether T is normal, or perhaps more accurately, whether T is not normal. If T were not normal, this would mean that ...
Página 7
... side a of a square whose area c is equal to the area of the circle r*T. The sides of the square must therefore equal a = r VT. But only certain line lengths can, under the specified conditions, be determined through geometric ...
... side a of a square whose area c is equal to the area of the circle r*T. The sides of the square must therefore equal a = r VT. But only certain line lengths can, under the specified conditions, be determined through geometric ...
Página 9
... side by side in a rectangle, they would appear as shown in the picture on the right. The greater the number of slices, the more the outline of the rectangle approximates the length of the circumference of the circle, while the height of ...
... side by side in a rectangle, they would appear as shown in the picture on the right. The greater the number of slices, the more the outline of the rectangle approximates the length of the circumference of the circle, while the height of ...
Página 15
... sides the polygons used have, the smaller the difference between these approximations. Archimedes began with regular hexagons and progressed through 12-, 24-and 48-sided polygons to polygons with 96 sides. Using this method he obtained ...
... sides the polygons used have, the smaller the difference between these approximations. Archimedes began with regular hexagons and progressed through 12-, 24-and 48-sided polygons to polygons with 96 sides. Using this method he obtained ...
Página 16
... sides in the polygons used for the calculations until by the end of this era of geometric approximation in 1630 AD, T was known to 39 decimal places. The second era began in the middle of the 17th century after the discovery of ...
... sides in the polygons used for the calculations until by the end of this era of geometric approximation in 1630 AD, T was known to 39 decimal places. The second era began in the middle of the 17th century after the discovery of ...
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