Source labels openChecked July 26, 2026

Erdős Problem 1084: Triangular Optimal D2

Erdős conjectured that the triangular lattice is best possible in 2D, in particular that $f_2(3n^2 + 3n + 1) < 9n^2 + 3n$ .

Convex geometry AMS 52

Mathematical statement

Erdős conjectured that the triangular lattice is best possible in 2D, in particular that $f_2(3n^2 + 3n + 1) < 9n^2 + 3n$ .

Note: in [Er75f] is read $9n^2 + 6n$ , but this seems to be a typo.

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_1084.variants.triangular_optimal_d2

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_1084.variants.triangular_optimal_d2 : f 2 (3 * n ^ 2 + 3 * n + 1) = 9 * n ^ 2 + 3 * n := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization erdosproblems.com/1084background