Inner parallel curves and domains in the equiaffine geometry (Q1261213)

In a previous paper [Analysis and geometry. Trends in research and teaching, 113-123 (1992; Zbl 0765.52008)] the author treated the definitions and properties of equiaffine inner parallel hypersurfaces in an \(n\)-dimensional affine space and compared them with the corresponding definitions and properties of Euclidean inner parallel hypersurfaces. These constructions become particularly obvious in the case of dimension 2, where many proofs strongly simplify and there exist instructive examples. It is the aim of this article to implement this program with the help of computer drawings together with an outlook on the inverse problem of determining outer equiaffine parallel curves, equivalent to the so-called dual billiard problem.