Affine.Simplex.circumcenter_eq_centroid
∀ {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] (s : Affine.Simplex ℝ P 1), s.circumcenter = Finset.centroid ℝ Finset.univ s.pointsThe circumcenter of a 1-simplex equals its centroid.
- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 2 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.
Cites32
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
- Norm.normproof · cited by 5,413
- Set.univproof · cited by 3,945
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- Nat.cast_oneproof · cited by 2,501
- HVAdd.hVAddproof · cited by 1,820
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- one_smulproof · cited by 1,374
- NormedAddTorsorstatement and proof · cited by 1,325
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Simplex.midpoint_faceOppositeCentroid_eulerPointproof · cited by 1