**PRINCE**: See now, whether pure fear and entire cowardice doth not make thee wrong this virtuous gentlewoman to close with us? Is she of the wicked? Is thine hostess here of the wicked? Or is thy boy of the wicked? Or honest Bardolph, whose zeal burns in his nose, of the wicked?
**POINS**: Answer, thou dead elm, answer.
**FALSTAFF**: The fiend hath prick’d down Bardolph irrecoverable; and his face is Lucifer’s privy-kitchen, where he doth nothing but roast malt-worms. For the boy- there is a good angel about him; but the devil outbids him too.
**PRINCE**: For the women?
**FALSTAFF**L For one of them- she’s in hell already, and burns poor souls. For th’ other- I owe her money; and whether she be damn’d for that, I know not.
>From _The Second Part of Henry the Fourth_ by Shakespeare.
New comment on your post #417 “A teaser”
Author : Negar
Comment:
Sariel just added you to Skype. Looking forward to finding you online 
Sariel just added you to Skype. Looking forward to finding you online !
New comment on your post #417 “A teaser”
Author : Sariel Har-Peled
Comment:
And here is a similar (and cuter) problem… Prove that the discrete hull of a convex body C of diameter Delta in the plane has O(\Delta^{2/3}) (real) vertices.
The discete hull is the convex hull of all the points of C inside the integer grid. A vertex of the convex hull would be considered to be real if it does not lie in the middle of an edge of the convex hull.
Similar claims hold in higher dimensions, but they are much harder to prove. Another cute problem is to prove that this bound is tight.
This question is from one my papers during my phd, but of course it was known to the greeks…. And there is an elegant and short proof.
And here is a similar (and cuter) problem… Prove that the discrete hull of a convex body C of diameter Delta in the plane has O(\Delta^{2/3}) (real) vertices.
The discete hull is the convex hull of all the points of C inside the integer grid. A vertex of the convex hull would be considered to be real if it does not lie in the middle of an edge of the convex hull.
Similar claims hold in higher dimensions, but they are much harder to prove. Another cute problem is to prove that this bound is tight.
This question is from one my papers during my phd, but of course it was known to the greeks…. And there is an elegant and short proof.
New comment on your post #417 “A teaser”
Author : Sariel Har-Peled
Comment:
Very nice. Way simpler than my solution…
Very nice. Way simpler than my solution…
New comment on your post #417 “A teaser”
Author : D. Eppstein
Comment:
P.S. that should be V^{1/d} both times. I assumed incorrectly that your comment section could handle html.
P.S. that should be V^{1/d} both times. I assumed incorrectly that your comment section could handle html.
New comment on your post #417 “A teaser”
Author : D. Eppstein
Comment:
If a maximal point m has one of its coordinates larger than V1/d, it can be charged to the points of U that it dominates along a line parallel to that coordinate; each point of U is charged O(d)=O(1) times. The remaining maximal points lie within a cube of dimensions V1/d and project to distinct points on one boundary facet of the cube.