An Area Inequality for Ellipses Inscribed in Quadrilaterals

نویسنده

  • ALAN HORWITZ
چکیده

If E is any ellipse inscribed in a convex quadrilateral, D – , then we prove that Area (E) Area(D – ) π 4 , and equality holds if and only if D – is a parallelogram and E is tangent to the sides of D – at the midpoints. We also prove that the foci of the unique ellipse of maximal area inscribed in a parallelogram, D – , lie on the orthogonal least squares line for the vertices of D – . This does not hold in general for convex quadrilaterals.

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تاریخ انتشار 2010