Computing Pi the Chudnovsky Way

summation steps

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.