Theorems · Theorem · geometry

EuclideanGeometry.Sphere.direction_orthRadius_le_iff

∀ {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] {s : EuclideanGeometry.Sphere P} {p q : P},
  (s.orthRadius p).direction ≤ (s.orthRadius q).direction ↔ ∃ r, q -ᵥ s.center = r • (p -ᵥ s.center)

Defined in

Mathlib.Geometry.Euclidean.Sphere.OrthRadius

Cited by

1 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor