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Results tagged with packing-and-covering
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user 5371
4
votes
Optimal packing of spheres tangent to a central sphere
This problem has been studied by many people in a general setting of convex bodies.
Given a convex body $K$ in $\mathbb R^d$ and an $\alpha > 0$, find the maximal number $H_{\alpha}(K)$ of nonover …
- 22.3k
56
votes
Accepted
Can we cover the unit square by these rectangles?
This problem actually goes back to Leo Moser.
The best result that I'm aware of is due to D. Jennings, who proved that all the rectangles of size $k^{-1} × (k + 1)^{-1}$, $k = 1, 2, 3 ...$, can be pac …
- 22.3k