Borwein's algorithm

Borwein's algorithm is an algorithm devised by Jonathan and Peter Borwein to calculate the value of 1/&pi.

It works as follows:

• Start out by setting

  

  

• Then iterate

  

  

Then a_k converges quartically against 1/π; that is, each iteration approximately quadruples the number of correct digits.

See also

• Borwein's algorithm (others) for an explanation of other algorithms by Jonathan and Peter Borwein to determine the digits of π.