Theorems · Definition · geometry
Affine.Simplex.circumcenter
{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 → PThe circumcenter of a simplex.
- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Sphere.centerproof · cited by 181
- Affine.Simplex.circumsphereproof · cited by 19
Cited by52
Results whose statement or proof uses this declaration.
- Affine.Simplex.mongePointproof · cited by 20
- Affine.Simplex.ninePointCircleproof · cited by 13
- Affine.Simplex.dist_circumcenter_eq_circumradiusstatement · cited by 12
- Affine.Simplex.pointsWithCircumcenterproof · cited by 10
- Affine.Simplex.circumcenter_mem_affineSpanstatement · cited by 8
- Affine.Simplex.eq_circumcenter_of_dist_eqstatement · cited by 5
- Affine.Simplex.dist_circumcenter_eq_circumradius'statement and proof · cited by 4
- Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenterstatement · cited by 4
- EuclideanGeometry.exists_circumcenter_eq_of_cospherical_subsetstatement · cited by 3
- Affine.Triangle.dist_orthocenter_reflection_circumcenterstatement and proof · cited by 3
- Affine.Simplex.ninePointCircle_centerstatement · cited by 3
- Affine.Simplex.circumcenter_mapstatement and proof · cited by 3