Theorems · Theorem · geometry

EuclideanGeometry.oangle_add_oangle_add_oangle_eq_pi

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] [inst_4 : Module.Oriented ℝ V (Fin 2)] [inst_5 : Fact (Module.finrank ℝ V = 2)]
  {p₁ p₂ p₃ : P},
  p₂ ≠ p₁ →
    p₃ ≠ p₂ →
      p₁ ≠ p₃ →
        EuclideanGeometry.oangle p₁ p₂ p₃ + EuclideanGeometry.oangle p₂ p₃ p₁ + EuclideanGeometry.oangle p₃ p₁ p₂ =
          ↑Real.pi

The sum of the angles of a triangle (possibly degenerate, where the triangle is a line), oriented angles at point.

Defined in

Mathlib.Geometry.Euclidean.Triangle

Cited by

0 results in Mathlib

Foundations

Depth 280 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorModule.OrientedFact