Theorems · Theorem · geometry

Orientation.oangle_eq_two_zsmul_oangle_sub_of_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 z : V},
  x ≠ y → x ≠ z → ‖x‖ = ‖y‖ → ‖x‖ = ‖z‖ → o.oangle y z = 2 • o.oangle (y - x) (z - x)

The angle at the center of a circle equals twice the angle at the circumference, oriented vector angle form.

Defined in

Mathlib.Geometry.Euclidean.Angle.Sphere

Cited by

1 results in Mathlib

Foundations

Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact