## Isoptics of a closed strictly convex curve.(English)Zbl 0739.53001

Global differential geometry and global analysis, Proc. Conf., Berlin/Ger. 1990, Lect. Notes Math. 1481, 28-35 (1991).
[For the entire collection see Zbl 0733.00014.]
The study of curves which are isoptical with respect to a given convex curve goes back to the beginning of this century. They are of interest in the theory of mechanisms.
The authors add some interesting new results to this theory. They give a simple description of the convexity of isoptics, establish conditions for a closed curve in order to be an isoptic of a suitable convex curve and present a simple construction for the tangents of isoptics. Furthermore their computations are used to derive some integral formulas of Crofton type including an interesting proof of the well-known Crofton formula as well.

### MSC:

 53A04 Curves in Euclidean and related spaces 52A10 Convex sets in $$2$$ dimensions (including convex curves)

### Keywords:

isoptics; convex curve; Crofton formula

Zbl 0733.00014