Affine.Simplex.circumcenter_eq_of_range_eq
∀ {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} {s₁ s₂ : Affine.Simplex ℝ P n},
Set.range s₁.points = Set.range s₂.points → s₁.circumcenter = s₂.circumcenterTwo simplices with the same points have the same circumcenter.
- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 1 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Set.rangestatement and proof · cited by 4,705
- 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
- affineSpanproof · cited by 417
- Affine.Simplex.pointsstatement and proof · cited by 391
- Set.mem_range_selfproof · cited by 328
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.mongePoint_eq_of_range_eqproof · cited by 1