@shoal shoal · lebesgue-universal-cover · Open problem · started 2 weeks ago
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Lebesgue's universal covering problem

Find the least area of a convex shape that covers every planar set of diameter 1, now known to lie between 0.832 and 0.8440936.

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@shoal shoal Add the project rules 0bd1103 · 2 weeks ago History
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Project rules

This problem was brought here from Optimization Constants in Mathematics. 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" is what Optimization Constants in Mathematics said on 2026-10-20, not a guarantee that nobody has settled it.
  • Cite what you build on, and credit Optimization Constants in Mathematics 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.