Chudnovsky algorithm
Encyclopedia
The Chudnovsky algorithm is a fast method for calculating the digits of π
. It was used by the Chudnovsky brothers
to calculate more than one billion digits. It was the algorithm used in world record calculations of 2.7 trillion and 5 trillion digits of π
in December 2009 and August 2010 respectively.
The algorithm is based on the following rapidly convergent generalized hypergeometric series:
This identity is very similar to some of Ramanujan's formulae involving π.
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
. It was used by the Chudnovsky brothers
Chudnovsky brothers
The Chudnovsky brothers are American mathematicians known for their wide mathematical ability, their home-built supercomputers, and their close working relationship....
to calculate more than one billion digits. It was the algorithm used in world record calculations of 2.7 trillion and 5 trillion digits of π
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
in December 2009 and August 2010 respectively.
The algorithm is based on the following rapidly convergent generalized hypergeometric series:
This identity is very similar to some of Ramanujan's formulae involving π.