Rendiconti del Seminario Matematico della Università di Padova


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Volume 133, 2015, pp. 159–172
DOI: 10.4171/RSMUP/133-8

$\alpha$-isoptics of a triangle and their connection to $\alpha$-isoptic of an oval

Małgorzata Michalska[1] and Witold Mozgawa[2]

(1) Uniwersytet Marii Curie-Skłodowskiej, Lublin, Poland
(2) Uniwersytet Marii Curie-Skłodowskiej, Lublin, Poland

For a fixed positive angle $\alpha$, $\alpha <\pi$ we get an explicit formulas for an $\alpha$-isoptic curve of a triangle and study some of its properties. We use obtained results to show that $\alpha$-isoptic of an oval is an envelope of $\alpha$-isoptics of properly chosen triangles.

Keywords: Isoptic curve, convex curve, support function, envelope, oval

Michalska Małgorzata, Mozgawa Witold: $\alpha$-isoptics of a triangle and their connection to $\alpha$-isoptic of an oval. Rend. Sem. Mat. Univ. Padova 133 (2015), 159-172. doi: 10.4171/RSMUP/133-8