EuclideanGeometry.Sphere.direction_orthRadius
∀ {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),
(s.orthRadius p).direction = (ℝ ∙ (p -ᵥ s.center))ᗮ- Cited by
- 5 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Submodule.spanstatement and proof · cited by 1,504
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspaceproof · cited by 871
- VSub.vsubstatement and proof · cited by 817
- AffineSubspace.directionstatement and proof · cited by 339
- Submodule.orthogonalstatement and proof · cited by 257
Cited by5
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iffproof · cited by 2
- EuclideanGeometry.Sphere.ncard_inter_orthRadius_eq_two_of_dist_lt_radiusproof · cited by 1
- EuclideanGeometry.Sphere.direction_orthRadius_le_iffproof · cited by 1