Affine.Simplex.circumradius_pos
∀ {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] {n : ℕ} (s : Affine.Simplex ℝ P (n + 1)), 0 < s.circumradiusThe circumradius of a simplex with at least two points is positive.
- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- Affine.Simplexstatement and proof · cited by 471
- Affine.Simplex.pointsproof · cited by 391
- lt_of_le_of_neproof · cited by 230
- Affine.Simplex.circumcenterproof · cited by 49
- Affine.Simplex.independentproof · cited by 45
- Affine.Simplex.circumradiusstatement and proof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.circumcenter_ne_pointproof · cited by 0