Theorems · Theorem · geometry

Orientation.oangle_sub_left_smul_rotation_pi_div_two

∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [hd2 : Fact (Module.finrank ℝ V = 2)]
  (o : Orientation ℝ V (Fin 2)) {x : V},
  x ≠ 0 → ∀ (r : ℝ), o.oangle (x - r • (o.rotation ↑(Real.pi / 2)) x) x = ↑(Real.arctan r)

An angle in a right-angled triangle expressed using arctan, where one side is a multiple of a rotation of another by π / 2, version subtracting vectors.

Defined in

Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle

Cited by

0 results in Mathlib

Foundations

Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceFact