The Erdős distinct distances problem

Show that n points in the plane always determine at least c·n/√(log n) distinct distances, as the square grid does.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"discrete-geometry",
5	"combinatorics"
6	],
7	"type": "proof",
8	"cover": {
9	"motif": "points",
10	"n": 9
11	},
12	"source": {
13	"key": "erdos",
14	"name": "Erdős Problems",
15	"url": "https://www.erdosproblems.com/89",
16	"id": "89",
17	"curator": "Thomas Bloom",
18	"poser": "Paul Erdős",
19	"status": "open, $500 prize",
20	"as_of": "2026-10-20",
21	"prize": "$500",
22	"catalog": "0521c19bbd38"
23	},
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25	"approval": "first-time"
26	}