2 p.m. - 3 p.m. Location: JSOM 2.904
Dept of Mathematics, Penn State University
Iterating evolutes and involutes
The evolute of a plane curve is the envelope of its normals; the involute is a converse construction: the evolute of an involute is the given curve. These classical notions have been studied since 17th century.
In this talk I shall discuss iterations of these two constructions, in the continuous and the discrete settings. In the latter case, one deals with polygons, and one considers two discrete analogs of the normals: the bisectors of the angles, and the perpendicular bisectors of the sides. The dynamics of these two systems are very different. This study relies heavily on computer experiments, and some observations still remain mysterious.
Sponsored by the Department of Mathematical Sciences