Ramanujan's Perimeter of an Ellipse
Mark B. Villarino
TL;DR
This paper analyzes the accuracy of Ramanujan's approximation for the perimeter of an ellipse through detailed error analysis, highlighting its precision and limitations.
Contribution
It provides a comprehensive error analysis of Ramanujan's approximation, offering insights into its accuracy and potential improvements.
Findings
Ramanujan's approximation is highly accurate for most ellipses.
The error analysis quantifies the approximation's deviation from the true perimeter.
The study identifies conditions under which the approximation performs best.
Abstract
We present a detailed error analysis of Ramanujan's most accurate approximation to the perimeter of an ellipse.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · History and Theory of Mathematics