Theorems · Theorem · geometry

Orientation.oangle_map_complex

∀ {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)) (f : V ≃ₗᵢ[ℝ] ℂ),
  (Orientation.map (Fin 2) f.toLinearEquiv) o = Complex.orientation →
    ∀ (x y : V), o.oangle x y = ↑((starRingEnd ℂ) (f x) * f y).arg

The oriented angle on an oriented real inner product space of dimension 2 can be evaluated in terms of a complex-number representation of the space.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceFact