Theorems · Theorem · geometry

Orientation.rotation_eq_self_iff_angle_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 : V}, x ≠ 0 → ∀ (θ : Real.Angle), (o.rotation θ) x = x ↔ θ = 0

A rotation of a nonzero vector equals that vector if and only if the angle is zero.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation

Cited by

1 results in Mathlib

Foundations

Depth 278 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact