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== Algorithm ==
# Initial value setting: <math display="block">a_0 = 1\qquad b_0 = \frac{1}{\sqrt{2}}\qquad t_0 = \frac{1}{4}\qquad p_0 = 1.</math>
# Repeat the following instructions until the difference of <math>a_n</math> and <math>b_n</math> is within the desired accuracy: <math display="block"> \begin{align}
a_{n+1} & = \frac{a_n + b_n}{2}, \\
\\
b_{n+1} & = \sqrt{a_n b_n}, \\
\\
t_{n+1} & = t_n - p_n(a_{n}-a_{n+1})^2, \\
\\
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The algorithm has [[quadratic convergence]], which essentially means that the number of correct digits doubles with each [[iteration]] of the algorithm.
== Mathematical background ==
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