6
votes
1answer
151 views

Best and worst centrally symmetric convex covering shapes

Suppose you have a centrally symmetric convex 2D shape $C$ of area $A$, and you randomly throw down copies of $C$ on the plane so that each $C$-center lies within a given unit square $S$, until $S$ is ...
4
votes
1answer
150 views

Cover of a n-simplex with balls

Consider a n-simplex. For each edge (i,j), consider a n-ball, such that vertices i and j are antipodal on this ball. Is the simplex covered by the union of these balls? Thank you.
3
votes
0answers
52 views

Between Cover and Partition

In a cover problem, there is a complex shape (e.g. a polygon), and we have to find a set of simpler shapes (e.g. squares or rectangles), such that their union is exactly equal to the complex shape. A ...
3
votes
0answers
361 views

N-balls covering n-balls

This question is a follow-on question from: Covering a unit ball with balls half the radius The questions are these: Given an arbitrary dimension d, and a unit n-ball in d-dimensional Euclidean ...