Computing Pi the Chudnovsky Way

​
summation steps
1
1
π
≈12
1
∑
k=0
k
(-1)
(6k)!(13591409+545140134k)
(3k)!
3
(k!)
3k+
3
2
640320
number of digits matched: 27
π ≈ 3.14159265358979323846264338
The Chudnovsky algorithm generates 14 or more digits of
π
for every summation step. It has been used to achieve numerous world record calculations for
π
since it was published in 1989. As implemented here, Mathematica calculates an approximation to
1
π
=12
∞
∑
k=0
k
(-1)
(6k)!(13591409+545140134k)
(3k)!
3
(k!)
3k+
3
2
640320
for a number of summation steps that you set. The Demonstration shows how many total digits of
π
have been correctly computed as a result.

References

[1] D. Chudnovsky and G. Chudnovsky, "The Computation of Classical Constants," Proceedings of the National Academy of Sciences (PNAS89), Washington, DC, 1989. www.pnas.org/content/86/21/8178.full.pdf.
[2] Wikipedia. "Chudnovsky Algorithm." (Oct 22, 2013) en.wikipedia.org/wiki/Chudnovsky_algorithm.

Permanent Citation

Michael Stern
​
​"Computing Pi the Chudnovsky Way"​
​http://demonstrations.wolfram.com/ComputingPiTheChudnovskyWay/​
​Wolfram Demonstrations Project​
​Published: January 24, 2014