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
... Gauss's Mathematical Diary (1796–1814), in which the author demonstrates a connection between the computation of T and the arithmetic-geometric mean. After the first edition of our book on the fascinating Nil desparare.
... Gauss's Mathematical Diary (1796–1814), in which the author demonstrates a connection between the computation of T and the arithmetic-geometric mean. After the first edition of our book on the fascinating Nil desparare.
Página 7
... geometric construction using only compass and ruler. (On the other hand it is possible if the constraining conditions are varied. For example, in hyperbolic geometry there may well be a circle, i.e. one whose area is equal to T, which ...
... geometric construction using only compass and ruler. (On the other hand it is possible if the constraining conditions are varied. For example, in hyperbolic geometry there may well be a circle, i.e. one whose area is equal to T, which ...
Página 8
... geometry a straight line cannot be drawn with a ruler.) After Lindemann had resolved the problem of the Squaring the ... geometrical definition of the number. The popular rule that T is the circumference of a circle with diameter 1 is ...
... geometry a straight line cannot be drawn with a ruler.) After Lindemann had resolved the problem of the Squaring the ... geometrical definition of the number. The popular rule that T is the circumference of a circle with diameter 1 is ...
Página 9
... geometric definition of T, there are many other definitions, including ones drawn from quite different contexts. For example, T appears in interesting probability problems. What is the probability that a coin tossed an even number of ...
... geometric definition of T, there are many other definitions, including ones drawn from quite different contexts. For example, T appears in interesting probability problems. What is the probability that a coin tossed an even number of ...
Página 16
... 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 infinitesimal analysis and infinite expressions. A specific method, namely the arctan ...
... 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 infinitesimal analysis and infinite expressions. A specific method, namely the arctan ...
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