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Marden (1945, 1966) attributes what is now known as Marden's theorem to Siebeck (1864) and cites nine papers that included a version of the theorem. Dan Kalman won the 2009 Lester R. Ford Award of the Mathematical Association of America for his 2008 paper in the American Mathematical Monthly describing the theorem.
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
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] Pólya enumeration theorem.
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 ...
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; N. Nadel vanishing theorem; Nakano vanishing theorem; O. Oka coherence theorem; T. Torelli theorem This page was last edited on 24 July 2023, at ...
Marden's theorem shows how to find the foci of this ellipse. [56] This ellipse has the greatest area of any ellipse tangent to all three sides of the triangle. The Mandart inellipse of a triangle is the ellipse inscribed within the triangle tangent to its sides at the contact points of its excircles.