# Tagged Questions

Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.

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### Max number of points in a grid with distance to the origin between $d$ and $d+\sqrt{2}/2$, for some distance $d$? [closed]

Consider the square grid centered at the origin $\{-n,\ldots,n\}\times\{-n,...,n\}$. What is the value or an upper bound, as a function of $n$, of $\max f(d)$, where $d$ is the distance from some ...
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### Constant hole density on the area of a circle

I need to create about 100 (small) holes in a distributor plate (hole diam = 0.5 mm; plate diameter = 100 mm). The sm. holes should be distributed in such a way that the density (hole/area) is nearly ...
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### Maximal set on hypersphere that does not contain pairs of orthogonal vectors

Let R be a region on a hypersphere. Each point A of the hypersphere is associated with a vector pointing to A and with origin at the centre of the hypersphere. So let me identify each point with a ...
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### Generalization of the “double cap conjecture” to a vector space with complex field

The conjecture that I proposed in Maximal set on hypersphere that does not contain pairs of orthogonal vectors is in fact known as the "double cap conjecture", as noted by Guillaume Aubrun. See for ...
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### Radial tilings with variable area ratios

I was looking at this neat page on logarithmic spiral tilings when a question popped up: http://www.uwgb.edu/dutchs/symmetry/log-spir.htm It seems that in all of the tilings shown, the area of each ...
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### Homology of the subcomplexes of the “diamond shaped” sphere under 1-norm in $R^n$ as a simplicial complex
The 1-norm on $\mathbb{R}^n$ is defined by $\|v\| = |v_1| + |v_2| + \cdots + |v_n|$ for a vector $v = (v_1, \ldots, v_n) \in \mathbb R^n$. The unit sphere $S^{n-1}_1$ under the 1-norm is a simplicial ...
I am wondering if the statistics of self-avoiding random lattice-walks on $\mathbb{Z}^2$ that turn left or right at each step (i.e., they cannot continue the direction of the preceding step) have been ...