Is a convex plane body determined by an isoptic?
The set of points from which a (planar) convex body \(B\) is seen under a constant angle \(\nu\in(0,\pi)\) is called the \(\nu\)-isoptic of \(B\). This paper refers to the question when a (planar) convex body is determined by a \(\nu\)-isoptic of it. The author derives uniqueness results for ellipses, for special angles, for convex polygons and for rotationally symmetric convex bodies. In particular, it is shown that two planar convex bodies coincide if they have an isoptic with the same \(\nu\in (0,\pi)\) in common, where \(1-{\nu\over\pi}\) is irrational or rational with even numerator in its lowest terms, and that in the remaining cases two convex polygons with common isoptic coincide, and a common isoptic of two different rotationally symmetric convex bodies is a circle.
scientific article; zbMATH DE number 6010054