Isoptics of a closed strictly convex curve. II
[Part I was reviewed in Zbl 0739.53001.] This second part proves several interesting properties of isoptics of plane closed convex curves \(C\). Let \(C_\alpha\) denote the \(\alpha\)-isotopic of \(C\), i.e., the locus of points from which all of \(C\) is seen under the constant angle \(\pi-\alpha\). A Crofton-type integral formula is proved for the annulus enclosed by \(C\) and \(C_\alpha\), and it is used to derive a differential equation for the dependence of the area of this annulus from \(\alpha\). Relations between tangent directions to \(C_\alpha\) and directions of special chords of \(C\) are contained. The preservation of constant width is investigated. Some technical differential equations are derived at the end of the paper. The methods of proof are elementary.
scientific article; zbMATH DE number 1021759