Theorems · Theorem · geometry

Orientation.oangle_rotation_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 → ∀ (θ : Real.Angle), o.oangle ((o.rotation θ) x) y = o.oangle x y - θ

Rotating the first vector by θ subtracts θ from the angle between two vectors.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation

Cited by

3 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceFact