Theorems · Theorem · geometry

EuclideanGeometry.Sphere.isTangentAt_center_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} {as : AffineSubspace ℝ P},
  s.IsTangentAt s.center as ↔ s.radius = 0 ∧ s.center ∈ as

Defined in

Mathlib.Geometry.Euclidean.Sphere.Tangent

Cited by

0 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor