Problem #1086 asks for $g(n)$, the minimal value such that any set of $n$ points in $\mathbb{R}^2$ contains at most $g(n)$ triangles of equal area.
The natural integer sequence is $g(3), g(4), g(5), \ldots$. This is a counting analog of the unit-distance problem (#90/A186705) and the distinct-distance problem (#89/A186704) — but for triangle area multiplicity rather than pairwise distance.
A search of OEIS did not surface this sequence. There are some related sequences (e.g., A051602 for same-shape triangles, A186926 for same-area lattice configurations) but none match the geometric extremal definition exactly.
Computing $g(n)$ for small $n$ requires enumerating point configurations and computing all $\binom{n}{3}$ triangle areas — non-trivial but should be tractable to $n \approx 10$ - $15$. Per the project's no-AI-submissions rule, a human-written computation would be needed before any OEIS submission.
(Filed alongside PRs #292-296 in the same Tier-1 OEIS-linking pass.)
Problem #1086 asks for$g(n)$ , the minimal value such that any set of $n$ points in $\mathbb{R}^2$ contains at most $g(n)$ triangles of equal area.
The natural integer sequence is$g(3), g(4), g(5), \ldots$ . This is a counting analog of the unit-distance problem (#90/A186705) and the distinct-distance problem (#89/A186704) — but for triangle area multiplicity rather than pairwise distance.
A search of OEIS did not surface this sequence. There are some related sequences (e.g., A051602 for same-shape triangles, A186926 for same-area lattice configurations) but none match the geometric extremal definition exactly.
Computing$g(n)$ for small $n$ requires enumerating point configurations and computing all $\binom{n}{3}$ triangle areas — non-trivial but should be tractable to $n \approx 10$ - $15$ . Per the project's no-AI-submissions rule, a human-written computation would be needed before any OEIS submission.
(Filed alongside PRs #292-296 in the same Tier-1 OEIS-linking pass.)