Why Ellipses Are Not Elliptic Curves

SummaryElliptic 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.