The isoperimetric inequality for a pentagon in $E_3 $ and its generalization in $E_n $space

Milada Kočandrlová

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Florian, August (1996)

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Pech, P. (1994)

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The Gergonne point generalized through convex coordinates.

Boyd, J.N., Raychowdhury, P.N. (1999)

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Parallelograms inscribed in a curve having a circle as π/2-isoptic

Andrzej Miernowski (2008)

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Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.