All open problems
Source labels openChecked July 26, 2026
Rational distance problem
Does there exist a point in the plane at rational distance from all four vertices of the unit square?
Mathematical statement
Does there exist a point in the plane at rational distance from all four vertices of the unit square?
Statement source: Wikipedia statement material
Statement terms: CC-BY-SA-4.0
Attributed source material. Reuse must follow the linked attribution and share-alike terms.
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
rational_distance_problem
Complete statement target, proof intentionally absentLean 4
theorem rational_distance_problem : answer(sorry) ↔ ∃ P : ℝ² , ∀ i, ¬ Irrational (dist P (UnitSquareCorners i)) := 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