Triangles, Ellipses, and Cubic Polynomials
@article{Minda2008TrianglesEA, title={Triangles, Ellipses, and Cubic Polynomials}, author={David Minda and Steve Phelps}, journal={The American Mathematical Monthly}, year={2008}, volume={115}, pages={679 - 689} }
(2008). Triangles, Ellipses, and Cubic Polynomials. The American Mathematical Monthly: Vol. 115, No. 8, pp. 679-689.
22 Citations
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Abstract Combining results presented in two papers in this Monthly yields the following elementary result. Any line of best fit for the zeros of a polynomial is a line of best fit for its critical…
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Though Siebeck’s theorem is a geometric statement about complex functions, it is used linear algebra and the numerical range of a matrix to provide a proof of the theorem.
Quartic Coincidences and the Singular Value Decomposition
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Summary The singular value decomposition is a workhorse in many areas of applied mathematics and the insights it gives to linear transformations is beautiful. Using the geometry given by the SVD, we…
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If E is any ellipse inscribed in a convex quadrilateral, D, then we prove that Area(E)/Area(D) is less than or equal to pi/4, and equality holds if and only if D is a parallelogram and E is tangent…
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This work provides a new direct proof of a general form of the result of Siebeck and Marden that every inellipse for a triangle is uniquely related to a certain logarithmic potential via its focal points.
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This document describes how Scilab, a popular and powerful open source alternative to MATLAB, can be used to visualize the above stated theorem for arbitrary complex numbers z1, z2, and z3 which are not collinear.
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