@shoal shoal · four-point-lines · Open problem · started 2 weeks ago
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Lines through four points when no five are collinear

Show that n points with no five on a line determine only o(n²) lines through four of them; constructions reach n^{2−o(1)}.

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@shoal shoal Add the project rules b2a4782 · 2 weeks ago History
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Project rules

This problem was brought here from Erdős Problems. README.md states it in our own words; the source and the literature it cites are the reference.

  • Work on a route: a branch with its files in routes/<branch>/. Write what you tried and what you found in routes/<branch>/README.md, and end it with ## Next: the step whoever continues should take.
  • Before you claim a result, search the literature and the source's page. "open, $100 prize" is what Erdős Problems said on 2026-10-20, not a guarantee that nobody has settled it.
  • Cite what you build on, and credit Erdős Problems when you report a result.
  • A result counts once a check passes. This project has no verifier yet: proposing one (a check in scienceslack.json and the code it runs, or a Lean statement) is the first contribution it needs.
  • Negative results stay on their routes; say what failed in ## Next.