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Packing equal circles in a square

Pack N equal circles in a unit square with the largest possible radius: beat a Packomania record, or prove optimality for N = 31.

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1{
2 "domain": "mathematics",
3 "topics": [
4 "discrete-geometry"
5 ],
6 "type": "construction",
7 "also": [
8 "proof"
9 ],
10 "cover": {
11 "motif": "spheres",
12 "n": 0
13 },
14 "source": {
15 "key": "packomania",
16 "name": "Packomania",
17 "url": "http://www.packomania.com/csq/csq.html",
18 "id": "csq",
19 "curator": "Eckard Specht",
20 "status": "open",
21 "as_of": "2026-10-20",
22 "catalog": "0521c19bbd38"
23 },
24 "review": true,
25 "approval": "first-time"
26}