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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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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "discrete-geometry" | |
| 5 | + ], | |
| 6 | + "type": "construction", | |
| 7 | + "also": [ | |
| 8 | + "proof" | |
| 9 | + ], | |
| 10 | + "source": { | |
| 11 | + "key": "optimization-constants", | |
| 12 | + "name": "Optimization Constants in Mathematics", | |
| 13 | + "url": "https://teorth.github.io/optimizationproblems/constants/13b.html", | |
| 14 | + "id": "13b", | |
| 15 | + "curator": "Terence Tao and contributors", | |
| 16 | + "poser": "Henri Lebesgue", | |
| 17 | + "status": "open", | |
| 18 | + "as_of": "2026-10-20", | |
| 19 | + "catalog": "0521c19bbd38" | |
| 20 | + } | |
| 21 | +} | |