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import FormalConjecturesUtilRational distance problem
mathoverflow/418260 asked by user Yuan Yang
D19 in Unsolved Problems in Number Theory
by
namespace RationalDistanceProblem
open EuclideanGeometry
def UnitSquareCorners : Fin 4 → ℝ² :=
![!2[0, 0], !2[1, 0], !2[1, 1], !2[0, 1]]
Does there exist a point in the plane at rational distance from all four vertices of the unit square?
@[category research open, AMS 11 51]
theorem rational_distance_problem :
answer(sorry) ↔ ∃ P : ℝ² , ∀ i, ¬ Irrational (dist P (UnitSquareCorners i)) := ⊢ True ↔ ∃ P, ∀ (i : Fin 4), ¬Irrational (dist P (UnitSquareCorners i))
All goals completed! 🐙
end RationalDistanceProblem