A remarkable
series discovered by the
Indian mathematician
Srinivasa Ramanujan. It was one of the most accurate methods of determining
pi to a large amount of decimal places until the advent of the
Chudnovsky Series. It is still an amazing discovery, and a very
elegant representation of
pi. This series adds roughly eight digits per
term.
Gosper in 1985 computed 17 million terms of the continued fraction for
pi using this.
1/pi = 2sqrt(2) / 9801 * (sigma; n=0 to infinity) [( (4n)! / n!^4) * (1103 + 26390n) / (4 * 99)^4n]
I suppose it loses some of it's
elegance when represented in plain
ascii on
html, but hey...the
symmetry is beautiful, and the
simplicity is beguiling.