Erdős Problem #352
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is there some \(c > 0\) such that every measurable \(A \subseteq \mathbb{R}^2\) of measure \(\geq c\) contains the vertices of a triangle of area 1?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/352.Prizenone
Topicsgeometry
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/352
Attempts
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Exact exhaustive certificates prove f(N)=14,16,18,21,23,24,26,28,32,32,34,38,39,41,44,45,48,52,52 for N=8,...,26 in Koizumi's equivalent lattice model; an all-N construction also rules out any one O(N
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