N-ellipse
In geometry, the -ellipse is a generalization of the ellipse allowing more than two foci. -ellipses go by numerous other names, including multifocal ellipse, polyellipse, egglipse, -ellipse, and Tschirnhaus'sche Eikurve (after Ehrenfried Walther von Tschirnhaus). They were first investigated by James Clerk Maxwell in 1846. Given focal points in a plane, an -ellipse is the locus of points of the plane whose sum of distances to the foci is a constant . 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 of foci, the -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 formula_2, while if "n" is even the degree is formula_3 "n"-ellipses are special cases of spectrahedra.