Erdős Problem #96
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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The set of all possible numbers of unit distances determined by the vertices of a convex \(n\)-gon.
The **maximum number of unit distances** determined by the vertices of a convex \(n\)-gon. This function is often denoted as \(U_c(n)\) in combinatorics.
If \(n\) points in \(\mathbb{R}^2\) form a convex polygon then there are \(O(n)\) many pairs which are distance \(1\) apart.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/96.Attempts
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