Kolloquiumsvortrag von Herrn Prof. Otfried Cheong am 19. November 2019 um 14:00 Uhr[19.11.2019]
Im Rahmen des Informatikkolloquium laden wir am 19. November 2019 um 14:00 Uhr zu einem Vortrag von Prof. Otfried Cheong zum Thema „Convex Covers and Translation Covers“ ein.
Prof. Otfried Cheong, KAIST, School of Computing
Convex Covers and Translation Covers
Gebäude 3, H 005
19.11.2019 14:00 Uhr – 15:00 Uhr
In 1914, Lebesgue asked for a convex set of smallest possible area that can contain a con- gruent copy of every set of diameter one. The same question can be asked for other fami- lies T of planar shapes: What is the convex set of smallest possible area that contains a con- gruent 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.
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