Theorems · Theorem · geometry

Orientation.oangle_eq_zero_iff_oangle_rev_eq_zero

∀ {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}, o.oangle x y = 0 ↔ o.oangle y x = 0

The oriented angle between two vectors is zero if and only if the angle with the vectors swapped is zero.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Basic

Cited by

1 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact