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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