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. 
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22 Citations
Highly Influential Citations
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Background Citations
6
Methods Citations
2
Results Citations
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22 Citations

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Lines of Best Fit for the Zeros and for the Critical Points of a Polynomial
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Four Theorems with Their Foci on Ellipses
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Quartic Coincidences and the Singular Value Decomposition
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An Area Inequality for Ellipses Inscribed in Quadrilaterals
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The Geometry of Cubic Polynomials
Summary We study the critical points of a complex cubic polynomial, normalized to have the form p(z) = (z - 1)(z - r1)(z - r2) with |r1| = 1 |r2|. If Tγ denotes the circle of diameter passing through…
A Geometric Proof of the Siebeck–Marden Theorem
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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.
Visualizing Marden's theorem with Scilab
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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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During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality…
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A complete proof of Marden’s Theorem is obtained, requiring very little beyond standard topics from undergraduate mathematics, and spanning analytic geometry, linear algebra, complex analysis, calculus, and properties of polynomials.
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