The reverse Kakeya problem

Otfried Cheong

School of Computing, KAIST

School of Computing, KAIST

2017/3/20 Tue 5PM

We prove a generalization of Pal’s 1921 conjecture that 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 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.Tags: OtfriedCheong