(10) Challenge to Pi (Contemporary period)Dec 15, 2012
From the 17th century onwards, Machin-like formulae remained the best method for calculating Pi, but in 1914, the Indian genius mathematician, Ramanujan, found the unique formula which converged 8 digits every term. He died at the age of 32, and it remains unknown how he derived the formula.In 1987, the Chudnovsky brothers developed the similar formula. They built a hand made supercomputer in their home and competed fiercely with other teams to calculate Pi. In addition, in 1976, Salamin and Brent discovered the new formula for calculating Pi to a large number of digits by using the Gauss's arithmetic-geometric mean. This formula has quadratic convergence, and the number of correct digits is doubled every iteration, for example, 5, 10 and 20 digits. After 40 iterations, the number of correct digits is 1 trillion. In future it is anticipated that new super algorithms will compute Pi rapidly and precisely without relying on the performance of computers.
| Pi (Ramanujan's formula)|
 Pi (AGM method)