Algebraic curves | Conic sections
N-ellipse
In geometry, the n-ellipse is a generalization of the ellipse allowing more than two foci. n-ellipses go by numerous other names, including multifocal ellipse, polyellipse, egglipse, k-ellipse, and Tschirnhaus'sche Eikurve (after Ehrenfried Walther von Tschirnhaus). They were first investigated by James Clerk Maxwell in 1846. 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. Both are algebraic curves of degree 2. For any number n of foci, the n-ellipse is a closed, convex curve. The curve is smooth unless it goes through a focus. The n-ellipse is in general a subset of the points satisfying a particular algebraic equation. If n is odd, the algebraic degree of the curve is , while if n is even the degree is n-ellipses are special cases of spectrahedra. (Wikipedia).
