Theorems · Theorem · geometry

Orientation.oangle_neg_left

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
  (o : Orientation ℝ V (Fin 2)) {x y : V}, x ≠ 0 → y ≠ 0 → o.oangle (-x) y = o.oangle x y + ↑Real.pi

Negating the first vector passed to oangle adds π to the angle.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Basic

Cited by

4 results in Mathlib

Foundations

Depth 277 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact