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johndcook.com
Ramanujan approximation ellipse circumference
There's no elementary formula for the circumference of an ellipse, but there is an elementary approximation that is extremely accurate. An ellipse has equation (x/a)² (y/b)² = 1. If a = b, the ellipse reduces to a circle and the circumference is simply 2πa. But the general formula for circumference requires the hypergeometric function
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