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arXiv · 1607.02086

Ellipses of minimal eccentricity inscribed in midpoint diagonal quadrilaterals

Alan Horwitz
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Abstract

In an earlier paper of the author, we showed that there is a unique ellipse of minimal eccentricity, $E_I$, inscribed in any convex quadrilateral, $Q$. Using a different approach in this paper, we prove that there is a unique ellipse of minimal eccentricity, $E_I$, inscribed in a midpoint diagonal quadrilateral, $Q$, which is a quadrilateral with the property that the intersection point of the diagonals of $Q$ coincides with the midpoint of at least one of the diagonals of $Q$. Our main result is that if $Q$ is a midpoint diagonal quadrilateral, then the smallest non-negative angle between equal conjugate diameters of $E_I$ equals the smallest non-negative angle between the diagonals of $Q$. This was proven in another earlier paper of the author for parallelograms.

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Alan Horwitz. 2016-07-07. Ellipses of minimal eccentricity inscribed in midpoint diagonal quadrilaterals. https://arxiv.org/abs/1607.02086

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