n-ellipse

In geometry, the n-ellipse is a generalization of the ellipse allowing more than two foci.

[1] n-ellipses go by numerous other names, including multifocal ellipse,[2] polyellipse,[3] egglipse,[4] k-ellipse,[5] and Tschirnhaus'sche Eikurve (after Ehrenfried Walther von Tschirnhaus).

[6] Given n focal points (ui, vi) in a plane, an n-ellipse is the locus of points of the plane whose sum of distances to the n foci is a constant d. In formulas, this is the set The 1-ellipse is the circle, and the 2-ellipse is the classic ellipse.

For any number n of foci, the n-ellipse is a closed, convex curve.[2]: (p.

[5]: p.7 The n-ellipse is in general a subset of the points satisfying a particular algebraic equation.[5]: Figs.