Theorems · Theorem · geometry

Orientation.rotation_oangle_eq_iff_norm_eq

∀ {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.rotation (o.oangle x y)) x = y ↔ ‖x‖ = ‖y‖

Rotating a vector by the angle to another vector gives the second vector if and only if the norms are equal.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation

Cited by

1 results in Mathlib

Foundations

Depth 279 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact