Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter
∀ {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 =
(Finset.affineCombination ℝ Finset.univ s.pointsWithCircumcenter) (Affine.Simplex.pointWeightsWithCircumcenter i)A single vertex, in terms of pointsWithCircumcenter.
- Defined in
- Mathlib.Geometry.Euclidean.Circumcenter
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 192 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.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineMapstatement · cited by 674
- Affine.Simplexstatement and proof · cited by 471
- Affine.Simplex.pointsstatement · cited by 391
- Finset.mem_univproof · cited by 361
- Finset.affineCombinationstatement and proof · cited by 159
Cited by1
Results whose statement or proof uses this declaration.
- Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsubproof · cited by 1