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On the centrally symmetric ovals circumscribing invariant maximal quadrilaterals


Abstract


If in a centrally symmetric oval all the inscribed convex quadrilaterals of maximal area and/or perimeter have the property that for any point on the oval there is exactly one such quadrilateral having that point as a vertex, does the oval have to be an ellipse? In this paper we will give an answer ranging from partial to complete to this multiple question

DOI Code: 10.1285/i15900932v32n2p35

Keywords: Oval; ellipse; quadrilateral; area; perimeter

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