Rendiconti del Seminario Matematico della Università di Padova


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Volume 125, 2011, pp. 39–49
DOI: 10.4171/RSMUP/125-3

Published online: 2011-06-30

An Integral Formula Related to Inner Isoptics

Horst Martini[1] and Witold Mozgawa[2]

(1) Technische Universität Chemnitz, Germany
(2) Uniwersytet Marii Curie-Skłodowskiej, Lublin, Poland

An isoptic $C_\alpha$ of a strictly convex $C^2$-curve in the plane is the locus of all points from which $C$ is seen under the same fixed angle. The two supporting lines of $C$ through such a point determine a secant of $C$, and the envelope of all these secants is the inner isoptic of $C$ and $C_\alpha$. We describe an integral formula for inner isoptics in terms of quantities that naturally occur in this geometric configuration.

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Martini Horst, Mozgawa Witold: An Integral Formula Related to Inner Isoptics. Rend. Sem. Mat. Univ. Padova 125 (2011), 39-49. doi: 10.4171/RSMUP/125-3