Inequalities for the Perimeter of an Ellipse
By Roger W. Barnard, K. Pearce, L. Schovanec. 2001
65 citations recorded by the source corpus.
Let a, b denote the lengths of the semi-major and -minor axes of an ellipse with eccentricity e = (1/a) √ a2 − b2 and whose perimeter is L(a, b) . The problem of approximating L(a, b) is an ancient one. An excellent account of this problem is found in a monthly article by G. Almkvist and B. Berndt [1]. In the article [1], several approximations that have been proposed over a period of nearly 4 centuries are presented. The approximation for L(a, b)/(π(a + b))
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/05169ff98fbc9db2b81daf44f4b7bac7704fc098
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In Algebra and Number Theory
In Geometry and Topology
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Citations in the corpus
- Optimal combinations bounds of root-square and arithmetic means for Toader mean (2012, background): “In recent past, the complete elliptic integrals have been a subject of intensive research [6–9, 11, 21].”
- Full length article: Bounds for the perimeter of an ellipse (2012, background): “During the past few centuries, many easily computable approximations to L(a, b) have been suggested by a large number of mathematicians [6–9,12,17].”