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Erdős problem 633

A triangle whose side lengths and angles are integrally independent is cuttable only into a non-zero square number of congruent triangles. This is proved in [So09c].

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FormalConjectures/ErdosProblems/

633.lean

Retained formal statement3 of 8

A triangle whose side lengths and angles are integrally independent is cuttable only into a non-zero square number of congruent triangles. This is proved in [So09c].

FormalConjectures/ErdosProblems/633.leanErdos633.isCuttable_iff_isSquare_of_linearIndependent8 linesExact file
∀ {n : ℕ} {T : Affine.Triangle ℝ (EuclideanSpace ℝ (Fin 2))},  LinearIndependent      ![dist (T.points 0) (T.points 1), dist (T.points 1) (T.points 2), dist (T.points 2) (T.points 0)] →    LinearIndependent        ![EuclideanGeometry.angle (T.points 0) (T.points 1) (T.points 2),          EuclideanGeometry.angle (T.points 1) (T.points 2) (T.points 0),          EuclideanGeometry.angle (T.points 2) (T.points 0) (T.points 1)] →      (Erdos633.IsCuttable n Tn ≠ 0 ∧ IsSquare n)
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