# Lecture by Otfried Cheong (Universität Bayreuth): Convex Covers and Translation Covers

In 1914, Lebesgue asked for a convex set of smallest possible area that can contain a congruent copy of every set of diameter one. The same question can be asked for other families T of planar shapes: What is the convex set of smallest possible area that contains a congruent copy of every element of T? Such a set is then called a convex cover for T, and we will see what smallest-area convex covers for some families of triangles look like. A translation cover for a family T of planar shapes is defined similarly: Z is a translation cover for T if every element of T can be translated into Z. Kakeya's celebrated needle problem, first posed in 1917, turns out to be a question about a smallest-area translation cover. We will see that the generalization of Kakeya's problem to other shapes is also a translation cover problem.

### Time & Location

Oct 21, 2019 | 02:15 PM

Freie Universität Berlin

Institut für Informatik

Takustr. 9

14195 Berlin

Room 005 (Ground Floor)