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Multifocal 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 : \left\. 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 2^n, while if ''n'' is even the degree is 2^n - \binom.J. Nie, P.A. Parrilo, B. Sturmfels:J. Nie, P. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 : \left\. 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 2^n, while if ''n'' is even the degree is 2^n - \binom.J. Nie, P.A. Parrilo, B. Sturmfels:J. Nie, P. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
