Theorems · Theorem · geometry

Sbtw.oangle_eq_add_pi_left

∀ {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] [hd2 : Fact (Module.finrank ℝ V = 2)] [inst_4 : Module.Oriented ℝ V (Fin 2)]
  {p₁ p₁' p₂ p₃ : P},
  Sbtw ℝ p₁ p₂ p₁' → p₃ ≠ p₂ → EuclideanGeometry.oangle p₁ p₂ p₃ = EuclideanGeometry.oangle p₁' p₂ p₃ + ↑Real.pi

Replacing the first point by one on the same line but the opposite ray adds π to the oriented angle.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Affine

Cited by

3 results in Mathlib

Foundations

Depth 286 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFactModule.Oriented