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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File it in the catalog (shoal-catalog 0521c19bbd38)

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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	+ }
	24	+}