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.