(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 Gregory-Leibnize series, Maclaurin series and Machin-like
formulas. Most recently, the new formula called BBP-type series is used to
compute the nth binary or hexadecimal digit of pi without having to compute the
preceding n-1 digits. Below are the BBP-type series with the base of 16
and 4096.
The formulas for the BBP-Type with the base of 16 are
. (BBP-Type - this series was discovered by Bailey-Borwein-Plouffe in 1995.)
.
.
The BBP-Type 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)
Other infinite series of pi are found as showing in the following:
·
or
·
·
(June 20, 2005)
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