Theorems · Theorem · geometry

Orientation.oangle_eq_neg_angle_of_sign_eq_neg_one

∀ {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).sign = -1 → o.oangle x y = -↑(InnerProductGeometry.angle x y)

The oriented angle between two vectors equals minus the unoriented angle if the sign is negative.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Basic

Cited by

1 results in Mathlib

Foundations

Depth 281 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact