Borwein's algorithm is an algorithm devised by Jonathan and Peter Borwein to calculate the value of 1/π. Flowcharts are often used to represent algorithms. ... Jonathan M. Borwein (1951-) was Shrum Professor of Science (1993-2003) and a Canada Research Chair in Information Technology (2001-08) at Simon Fraser University, and was founding Director of the Centre for Experimental and Constructive Mathematics. ... Peter B. Borwein is a Canadian mathematician, co-developer of algorith for calculating π to nth digit, co-discoverer of billionth, four billionth, 40th billionth, and quadrillionth digits of π, and professor at Simon Fraser University. ... The minuscule, or lower-case, pi The mathematical constant π is commonly used in mathematics and physics. ...
It works as follows:
Start out by setting
Then iterate
Then ak 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.
Gauss-Legendre algorithm - another algorithm to calculate pi
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