# Questions tagged [packing-problem]

Questions on the packing of various (two- or three-dimensional) geometric objects.

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### How is those cases trivial in packing L's in Tans

In packing problem "L's in Tans" as presented on https://www2.stetson.edu/~efriedma/Lintan/. I don't understand how is some cases trivial and others are not. For example case $n=4$ isn't ...
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### Packing L's in Tans and L's in L's

I'm a young researcher and I'm pretty new in this field. I want to work on packing problem "L's in Tans" and "L's in L's" as presented on https://www2.stetson.edu/~efriedma/...
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### uniform rectangle packing

I'm wondering if there is a formula or algorithm how many uniform rectangles of size $a\times b$ I can put in a square of size $c\times c$. Does anyone have a hint for literature?
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### Upper bound on minimum distance between $n$ points on unit sphere [duplicate]

Suppose we have $n$ points $x_1,\ldots, x_n$ on the unit sphere in $\mathbb{R}^3$ (i.e. $\left\lVert x_i \right\rVert_2 = 1$). Is there a tight upper bound, as a function of $n$, on the minimum ...
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### What seating configuration respects Covid-19 distancing but provides maximum packing?

I am a musician who plays in Celtic sessions. Typically 5 to 20 of us crowd into a pub or living room, but due to Covid-19 physical distancing recommendations, we now have to play outside in a big ...
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### A compact set is negligible iff its packing number tends to $0$ as packing bound tends to $0$

A set $S$ is called epsilon separated if for any distinct $x$ and $y$ in $S$, $|x-y|>\epsilon$. Let be $K$ a compact set in $\mathbb{R}^n$, and let's define $P(K,\epsilon)$ as the maximum number of ...
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### What are Voronoi cells for FCC and HCP Lattices lattices in space?

What are Vornoi cells for FCC and HCP Lattices ? (See plot below for FCC and HCP). Is my uderstanding correct that we should get one of the 5 "parallelohedra" ? If so, that seems to contradict ...
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### Is it possible to fit more than 23 dots in a 7 by 8 rectangle?

For practical reasons I would like to know how many dots you can fit in an $7 \times 8$ box with no two dots closer than 2 metres from each other. The simplest arrangement has 4 dots along each row ...
47 views