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Carbery's rectangle problem
Show that an open subset of the unit square with area α contains the corners of an axis-parallel rectangle of area at least cα².
| 1 | { |
| 2 | "domain": "mathematics", |
| 3 | "topics": [ |
| 4 | "analysis", |
| 5 | "combinatorics" |
| 6 | ], |
| 7 | "type": "proof", |
| 8 | "source": { |
| 9 | "key": "green-100", |
| 10 | "name": "Ben Green's 100 open problems", |
| 11 | "url": "https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.85", |
| 12 | "id": "85", |
| 13 | "curator": "Ben Green", |
| 14 | "poser": "Anthony Carbery, Michael Christ and James Wright", |
| 15 | "status": "open", |
| 16 | "as_of": "2026-10-20", |
| 17 | "catalog": "0521c19bbd38" |
| 18 | } |
| 19 | } |