Abstract
We give a constructive proof for the existence of inscribed families of ellipses in triangles and convex quadrilaterals; a unique ellipse exists in a convex pentagon. The techniques employed are based upon duality principles. One by-product of this approach is that the ellipse inscribed in a pentagon and that inscribed in its diagonal pentagon are algebraically related; they are as intrinsically linked as are the pentagon and its diagonal pentagon.
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The authors would like to thank the referees for their comments. We believe that they simultaneously improved our exposition and provided a deeper context for our work.
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Communicated by Doron Lubinsky.
Dedicated to Professor Ed Saff on his 70th birthday, with admiration and gratitude.
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Agarwal, M., Clifford, J. & Lachance, M. Duality and Inscribed Ellipses. Comput. Methods Funct. Theory 15, 635–644 (2015). https://doi.org/10.1007/s40315-015-0124-0
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DOI: https://doi.org/10.1007/s40315-015-0124-0