Affine.Simplex.mem_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} (s : Affine.Simplex ℝ P n) (i : Fin (n + 1)), s.points i ∈ s.circumsphereAll points lie in the circumsphere.
- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Affine.Simplex.pointsstatement · cited by 391
- EuclideanGeometry.Spherestatement · cited by 233
- Affine.Simplex.circumspherestatement · cited by 19
- Affine.Simplex.dist_circumcenter_eq_circumradiusproof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- EuclideanGeometry.cospherical_of_two_zsmul_oangle_eq_of_not_collinearproof · cited by 2
- Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradiusproof · cited by 2
- EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eqproof · cited by 1
- Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradiusproof · cited by 0
- Affine.Triangle.mem_circumsphere_of_two_zsmul_oangle_eqproof · cited by 0