The reverse Kakeya problem
Abstract We prove a generalization of Pál'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° inside Q. We also prove a lower bound of Ω(m n 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.
1998 ◽
Vol 58
(1)
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pp. 1-13
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Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
2016 ◽
Vol 26
(12)
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pp. 1650204
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1953 ◽
Vol 49
(1)
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pp. 59-62
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