Dual curves to isoptics of ovals

Abstract

Isoptic curves have been known and studied since the 18th century. Nowadays they have been examined inter alia by Benko, Cie´slak, G´o´zd´z, Miernowski and Mozgawa in many papers for example in [1], [2], [3] and [7]. We want to propose a new point of view isoptics. For a given oval we consider a dual curve on Blaschke cylinder and we construct a dual curve for its isoptic. Some properties, for example the loss of convexity is easier to observe on the dual curve than on the given curve. From the analysis of properties of dual curves to isoptics we get a new form of the condition for the convexity of isoptic curves.