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Results tagged with discrete-geometry
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user 104330
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
28
votes
Accepted
Does a function from $\mathbb R^2$ to $\mathbb R$ which sums to 0 on the corners of any unit...
The answer is yes, I learned this from the paper that appeared on arXiv literally yesterday https://arxiv.org/abs/2403.01279, they quote
R. Katz, M. Krebs and A. Shaheen, Zero sums on unit square vert …
- 6,476
12
votes
Accepted
Is the maximal packing density of identical circles in a circle always an algebraic number?
Yes indeed, they are all algebraic. The idea is that we can describe the critical $r$ as a first-order formula in the language of fields, something like
$$\forall r_1\quad ((0 < r_1 \wedge r_1 \le r)\ …
- 6,476