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.
For any number n of foci, the n-ellipse is a closed, convex curve.:(p. 90) The curve is smooth unless it goes through a focus.:p.7 If n is odd, the algebraic degree of the curve is , while if n is even the degree is .:(Thm. 1.1)
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- James Clerk Maxwell (1846): "Paper on the Description of Oval Curves, Feb 1846, from The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862