Theorems · Theorem · geometry

EuclideanGeometry.sin_pos_of_not_collinear

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {p₁ p₂ p₃ : P},
  ¬Collinear ℝ {p₁, p₂, p₃} → 0 < Real.sin (EuclideanGeometry.angle p₁ p₂ p₃)

If three points are not collinear, the sine of the angle between them is positive.

Defined in

Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine

Cited by

2 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor