Affine.Simplex.dist_point_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] {n : ℕ} [inst_4 : NeZero n] (s : Affine.Simplex ℝ P n) (i : Fin (n + 1)),
dist (s.points i) s.centroid = ↑n * dist s.centroid (s.faceOppositeCentroid i)The distance from a vertex to the centroid equals n times the distance from the centroid
to the corresponding faceOppositeCentroid.
- Defined in
- Mathlib.Geometry.Euclidean.Simplex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- VSub.vsubproof · cited by 817
- Affine.Simplexstatement and proof · cited by 471
- Affine.Simplex.pointsstatement and proof · cited by 391
- norm_smulproof · cited by 242
- dist_eq_norm_vsubproof · cited by 76
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Triangle.dist_point_centroidproof · cited by 0