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

Andrzej Miernowski (2008)

Annales UMCS, Mathematica

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.

Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces

De Beule, J., Metsch, K., Klein, A., Storme, L. (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 05B25, 51E20.We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces.The research of the fourth author was also supported by the Project Combined algorithmic...

Pentagramma mirificum and elliptic functions (Napier, Gauss, Poncelet, Jacobi, ...)

Vadim Schechtman (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

We give an exposition of unpublished fragments of Gauss where he discovered (using a work of Jacobi) a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in elliptic functions of the classical dilogarithm five-term relation.

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