Problem 99

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Statement. Let $A\subseteq\mathbb{R}^2$ be a set of $n$ points with minimum distance equal to 1, chosen to minimise the diameter of $A$. If $n$ is sufficiently large then must there be three points in $A$ which form an equilateral triangle of size 1?

Status. Open.

Source. erdosproblems.com/99, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #99, https://www.erdosproblems.com/99.

References.

• [BeFo99] Bezdek, András and Fodor, Ferenc, Minimal diameter of certain sets in the plane. J. Combin. Theory Ser. A (1999), 105-111.
• [Er94b] Erdős, Paul, Some problems in number theory, combinatorics and combinatorial geometry. Math. Pannon. (1994), 261-269.

Formalization. Statement in formal-conjectures.

Progress

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Known Results

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Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

• erdos_1994_some_problems_number_theory_combinatorics_combinatorial_geometry
• erdos_1995_my_favourite_problems_number_theory_combinatorics