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Results tagged with discrete-geometry
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user 90655
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
10
votes
Why do bees create hexagonal cells ? (Mathematical reasons)
Here is a paragraph of THE LIFE OF THE BEE (1901) By Maurice Maeterlinck:
"There are only," says Dr. Reid, "three possible figures of the cells which can make them all equal and similar, without any …
- 4,195
4
votes
1
answer
193
views
Two questions on "Table problem on $\Bbb S^2$"
The following conjecture is known as "Table problem on $\Bbb S^2$"
Conjecture (Table problem on $\Bbb S^2$): Suppose $x_1, x_2,x_3,x_4 \in\Bbb S^2 \subseteq \Bbb R^3$ are the vertices of a
squar …
- 4,195
3
votes
1
answer
161
views
Distance relation among points in high-dimensional hypercubes
Let $Q_{4n-1}$ be a unit hypercube of dimension $4n-1$. Has the following statement been proven?
There are $4n$ vertices in $Q_{4n-1}$ such that the distance between each pair of them is $2\sqrt{ …
- 4,195
0
votes
1
answer
145
views
Is Kakutani's Theorem true for the Euclidean plane? [closed]
The following analogue of Kakutani's theorem has been proved by F. J. Dyson (MR44620)
Theorem (F. J. Dyson 1951): Let $\Bbb S^2$ be the surface of a sphere with center $Z$ in Euclidean $3$-space …
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