The reverse Kakeya problem

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We prove a generalization of Pal's conjecture from 1921: if a convex shape P can be placed in any orientation inside a convex shape Q in the plane, then P can also be turned continuously through 360 degrees inside Q. We also prove a lower bound of Omega(mn(2)) on the number of combinatorially distinct maximal placements of a convex m-gon P in a convex n-gon Q. This matches the upper bound proven by Agarwal et al.
Publisher
WALTER DE GRUYTER GMBH
Issue Date
2021-01
Language
English
Article Type
Article
Citation

ADVANCES IN GEOMETRY, v.21, no.1, pp.75 - 84

ISSN
1615-715X
DOI
10.1515/advgeom-2020-0030
URI
http://hdl.handle.net/10203/281664
Appears in Collection
CS-Journal Papers(저널논문)
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