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DESCRIPTION: 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 s
ame question can be asked for other families T of planar shapes: What is th
e convex set of smallest possible area that contains a congruent copy of ev
ery element of T? Such a set is then called a convex cover for T\, and we w
ill see what smallest-area convex covers for some families of triangles loo
k like. A translation cover for a family T of planar shapes is defined simi
larly: Z is a translation cover for T if every element of T can be translat
ed 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 trans
lation cover problem.
DTSTAMP:20191025T172800
DTSTART:20191021T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Otfried Cheong (Universität Bayreuth): Convex Covers and Translatio
n Covers
UID:95691410@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20191021-L-Cheong.html
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