Ellipses of minimal eccentricity inscribed in midpoint diagonal quadrilaterals
Abstract
In an earlier paper of the author, we showed that there is a unique ellipse of minimal eccentricity, EI, inscribed in any convex quadrilateral, Q. Using a different approach in this paper, we prove that there is a unique ellipse of minimal eccentricity, EI, 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 EI 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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