Theorems · Definition · geometry
Affine.Simplex.circumsphere
{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} → Affine.Simplex ℝ P n → EuclideanGeometry.Sphere PThe circumsphere of a simplex.
- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NormedAddTorsorstatement and proof · cited by 1,325
- Affine.Simplexstatement and proof · cited by 471
- EuclideanGeometry.Spherestatement · cited by 233
Cited by21
Results whose statement or proof uses this declaration.
- Affine.Simplex.circumcenterproof · cited by 49
- Affine.Simplex.circumradiusproof · cited by 35
- Affine.Simplex.circumsphere_unique_dist_eqstatement · cited by 6
- Affine.Simplex.mem_circumspherestatement · cited by 6
- Affine.Simplex.eq_circumcenter_of_dist_eqproof · cited by 5
- Affine.Simplex.eq_circumradius_of_dist_eqproof · cited by 3
- Affine.Simplex.circumsphere_reindexstatement and proof · cited by 2
- Affine.Triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eqstatement and proof · cited by 2
- EuclideanGeometry.cospherical_of_two_zsmul_oangle_eq_of_not_collinearproof · cited by 2
- EuclideanGeometry.exists_circumsphere_eq_of_cospherical_subsetstatement · cited by 2
- Affine.Simplex.circumcenter_reindexproof · cited by 2
- Affine.Triangle.circumsphere_eq_of_dist_of_oanglestatement · cited by 1