Theorems · Theorem · geometry

EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection

∀ {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 : P} {as : AffineSubspace ℝ P}
  [inst_4 : Nonempty ↥as] [inst_5 : as.direction.HasOrthogonalProjection],
  s.IsTangentAt p as → p = ↑((EuclideanGeometry.orthogonalProjection as) s.center)

Defined in

Mathlib.Geometry.Euclidean.Sphere.Tangent

Cited by

1 results in Mathlib

Foundations

Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptySubmodule.HasOrthogonalProjection