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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.mi.fu-berlin.de
URL:https://www.mi.fu-berlin.de/en/facetsofcomplexity/monday/20191021-L-Che
 ong.html
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