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A Property of Euler's Elastic Curve

Name: A Property of Euler's Elastic Curve
Keywords: Elliptic functions and integrals, Curves in Euclidean and related spaces, elliptic integral, History of mathematics in the 19th century, lemniscate, elastic curve

A property of Euler's elastic curve

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 2000Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Elemente der Mathematik, volume 55, pages 156-162 (issn: 0013-6018, eissn: 1420-8962,

Authors: Judith L. Nowalsky; Leonardo Solanilla; Pamela A. Neill; Victor H. Moll;

doi: 10.1007/s000170050081

A Property of Euler's Elastic Curve

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Abstract

Euler and Legendre found formulas for certain products of elliptic integrals. Legendre's proof is sketched, and Euler's method is generalized to prove a more general formula which may be interpreted as a property of a curve generalizing Euler's elastic curve.

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Keywords

Elliptic functions and integrals, Curves in Euclidean and related spaces, elliptic integral, History of mathematics in the 19th century, lemniscate, elastic curve

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