Theorems · Theorem · geometry

EuclideanGeometry.Sphere.center_mem_affineSpan_pair_iff_isDiameter

∀ {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} {p₁ p₂ : P},
  p₁ ∈ s → p₂ ∈ s → (s.center ∈ line[ℝ, p₁, p₂] ↔ s.IsDiameter p₁ p₂)

The center lies on the line through two points of a sphere if and only if those points are the endpoints of a diameter.

Defined in

Mathlib.Geometry.Euclidean.Sphere.Basic

Cited by

0 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor