Theorems · Definition · geometry

Polygon.toTriangle

(R : Type u_1) →
  {V : Type u_2} →
    {P : Type u_3} →
      [inst : Ring R] →
        [inst_1 : AddCommGroup V] →
          [inst_2 : Module R V] →
            [inst_3 : AddTorsor V P] → (p : Polygon P 3) → Polygon.HasNondegenerateVertices R p → Affine.Triangle R P

Convert a polygon with 3 nondegenerate vertices to an Affine.Triangle.

Defined in: Mathlib.Geometry.Polygon.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup Module AddTorsor

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
AddTorsorstatement and proof · cited by 1,657
Affine.Trianglestatement · cited by 75
Polygonstatement and proof · cited by 12
Polygon.verticesproof · cited by 5
Polygon.HasNondegenerateVerticesstatement and proof · cited by 5

Cited by3

Results whose statement or proof uses this declaration.

Polygon.toTriangle_pointsstatement · cited by 0
Polygon.toTriangle_toPolygonstatement and proof · cited by 0
Affine.Triangle.toPolygon_toTrianglestatement and proof · cited by 0