# Questions tagged [circle-packing]

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### Densest safe disk packing

Inspired by current regulations regarding the minimal distance to be kept among people to prevent spreading of the COVID-19 virus and the maximal number of people in a group that is not subjected to ...
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### Packing circles with radii 1, 2, 3, …, n in a rectangle

For each positive integer n, let $a_n$ be the area of the smallest rectangle whose area is a whole number, and inside which it is possible to pack all n circles of radii 1, 2, 3, ..., n respectively (...
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### Do kissing numbers with distance $d$ always grow polynomially or exponentially in dimension?

Let $A_d(n)$ be the largest number of points that can be packed on the $n$-unit sphere, such that every point is at least $d$ apart. Compare with, for instance, https://arxiv.org/abs/1507.03631 When ...
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### Six yolks in a bowl: Why not optimal circle packing? [closed]

Making soufflé tonight, I wondered if the six yolks took on the optimal circle packing configuration. They do not. It is only with seven congruent circles that the optimal packing places one in the ...
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Since 2013, I found Some problems on Apollonian Gasket as following. These problem also is higher level of Eppstein Point. I am looking for a proof of one of these problems: Let three $(A)$, $(B)$, $(... 1answer 216 views ### Some inequalities on chain of circle packing By my computation, I pose a conjecture as follows and I am looking for a proof: Conjecture: Let$(O)$be a circle with radius$R$, and$n$be positive integer$n\ge 3$. Construct$n$circles$(...
The problem of the expected density of a saturated random packing of unit circles in the plane can be described as follows. In a circular region $C$ of a large radius pick a point at random and draw ...