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Cassini oval

Class of quartic plane curves / From Wikipedia, the free encyclopedia

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In geometry, a Cassini oval is a quartic plane curve defined as the locus of points in the plane such that the product of the distances to two fixed points (foci) is constant. This may be contrasted with an ellipse, for which the sum of the distances is constant, rather than the product. Cassini ovals are the special case of polynomial lemniscates when the polynomial used has degree 2.

Cassini-3kurv.svg
Three Cassini ovals, differing by the range within which the parameter e (equal to b/a) falls:
  0 < e < 1
  e = 1
  1 < e < √2
Not shown: e ≥ √2 (convex).

Cassini ovals are named after the astronomer Giovanni Domenico Cassini who studied them in the late 17th century.[1] Cassini believed that the Sun traveled around the Earth on one of these ovals, with the Earth at one focus of the oval.[citation needed] Other names include Cassinian ovals, Cassinian curves and ovals of Cassini.