Erdős Problem 99
For sufficiently large n, is it the case that any set of n points with minimum distance that minimizes diameter must contain an equilateral triangle of side length 1?
Mathematical statement
For sufficiently large n, is it the case that any set of n points with minimum distance that minimizes diameter must contain an equilateral triangle of side length 1?
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_99
theorem erdos_99 : answer(sorry) ↔ ∀ᶠ n in Filter.atTop, ∀ A : Finset ℝ², A.card = n → HasMinDist1 A → (IsMinOn (fun B: Finset ℝ² => diam (B : Set ℝ²)) {B : Finset ℝ² | B.card = n ∧ HasMinDist1 B} A) → ∃ᵉ (p ∈ A) (q ∈ A) (r ∈ A), FormsEquilateralTriangle p q r := bysorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References