(Pi)
The constant pi, denoted
, is a real number and found everywhere in nature. The constant pi is known to be irrational and transcendental number. The precise pi is determined through the ages and its decimal is never ending. In nowadays the value of pi is known to more than one trillion places via the methods of the GregoryLeibnize series, Maclaurin series and Machinlike formulas.
Most recently, the new formula called BBPtype series is used to compute the n^{th }binary or hexadecimal digit of pi without having to compute the preceding n –1 digits. Below are the BBPtype series with the base of 16 and 4096.
The formulas for the BBPtype with the base of 16 are
 . (BBPType  this series was discovered by BaileyBorweinPlouffe in 1995.)
 .
 .
The BBPtype series formulas are found in the base of 4096 that causes the infinite series converges extraordinarily rapidly, namely
 .
(posted May 29, 2006)
 .
(posted July 4, 2006)
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Other infinite series of pi are found as showing in the following:
.
or
.
.
(June 20, 2005)
.
 .
(05/29/2006)
(07/04/2006  update)
(03/17/2009  update)
More Related Series
Main SMS
InText or Website Citation
Tue N. Vu, Pi, 07/04/2006, from Series Math Study Resource.
The mathematical rules of the universe are visible to men in the form of beauty.
(John Michel)
