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Why Ellipses Are Not Elliptic Curves

Adrian Rice and Ezra Brown
Mathematics Magazine
Vol. 85, No. 3 (June 2012), pp. 163-176
DOI: 10.4169/math.mag.85.3.163
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.85.3.163
Page Count: 14
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Why Ellipses Are Not Elliptic Curves
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Abstract

Summary Elliptic curves are a fascinating area of algebraic geometry with important connections to number theory, topology, and complex analysis. As their current ubiquity in mathematics suggests, elliptic curves have a long and fascinating history stretching back many centuries. This paper presents a survey of key points in their development, via elliptic integrals and functions, closing with an explanation of why no elliptically-shaped planar curved line may ever be called an elliptic curve.

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