Timeline for Splitting the $n$-cube into two small congruent convex halves

9 events

when toggle format	what		by	license	comment
Dec 28, 2016 at 17:19	vote	accept	Wlodek Kuperberg
Dec 28, 2016 at 17:19	vote	accept	Wlodek Kuperberg
Dec 28, 2016 at 17:19
Dec 28, 2016 at 17:19	vote	accept	Wlodek Kuperberg
Dec 28, 2016 at 17:19
Dec 28, 2016 at 16:25	answer	added	Ilya Bogdanov		timeline score: 1
Dec 28, 2016 at 12:26	answer	added	Markus Sprecher		timeline score: 4
Dec 28, 2016 at 9:12	comment	added	Markus Sprecher		If the hyperplane cuts an edge with ratio $x:1-x$ it will cut the opposite edge (i.e. the edge symmetric to the center of the cube) with ratio $1-x:x$. It follows that the diameter of a half is at least $\sqrt{(n-1)+x^2}$. Hence we see that the smallest possible diameter is $\sqrt{n-3/4}$ and that if a hyperplane with the smallest possible diameter cuts an edge it must cut it in half. Hence we are left with only finitely many cases.
Dec 28, 2016 at 0:30	history	edited	Wlodek Kuperberg	CC BY-SA 3.0	added 19 characters in body
Dec 28, 2016 at 0:22	history	edited	Wlodek Kuperberg	CC BY-SA 3.0	deleted 50 characters in body
Dec 28, 2016 at 0:05	history	asked	Wlodek Kuperberg	CC BY-SA 3.0