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Marden's theorem states that the red dots are the foci of the ellipse. In mathematics , Marden's theorem , named after Morris Marden but proved about 100 years earlier by Jörg Siebeck, gives a geometric relationship between the zeroes of a third-degree polynomial with complex coefficients and the zeroes of its derivative .
Morris Marden (1905–1991) was an American mathematician. ... He is known for the Marden's theorem, which was proven by Jörg Siebeck. [failed verification] [1]
The tameness theorem was conjectured by Marden (1974). It was proved by Agol (2004) and, independently, by Danny Calegari and David Gabai. It is one of the fundamental properties of geometrically infinite hyperbolic 3-manifolds, together with the density theorem for Kleinian groups and the ending lamination theorem.
Marden's theorem. This theorem relating the location of the zeros of a complex cubic polynomial to the zeros of its derivative was named by Dan Kalman after Kalman read it in a 1966 book by Morris Marden, who had first written about it in 1945. [8] But, as Marden had himself written, its original proof was by Jörg Siebeck in 1864. [9]
Marden's theorem; Maxwell's theorem (geometry) Menelaus's theorem; Midpoint theorem (triangle) Mollweide's formula; Morley's trisector theorem; N. Napoleon's theorem; P.
According to Marden's theorem, [3] if the three vertices of the triangle are the complex zeros of a cubic polynomial, then the foci of the Steiner inellipse are the zeros of the derivative of the polynomial. The major axis of the Steiner inellipse is the line of best orthogonal fit for the vertices. [6]: Corollary 2.4
The foci of a triangle's Steiner inellipse can be found as follows, according to Marden's theorem: [56] [57] Denote the triangle's vertices in the complex plane as a = x A + y A i, b = x B + y B i, and c = x C + y C i. Write the cubic equation () =, take its derivative, and equate the (quadratic) derivative to zero. Marden's theorem says that ...
Marcinkiewicz theorem (functional analysis) Marden's theorem (polynomials) Mazur's control theorem (number theory) Mergelyan's theorem (complex analysis) Marginal value theorem (biology, optimization) Markus−Yamabe theorem (dynamical systems) Martingale representation theorem (probability theory) Mason–Stothers theorem (polynomials)