Affine.Simplex.mongePoint_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 + 2)),
s.mongePoint =
(Finset.affineCombination ℝ Finset.univ s.pointsWithCircumcenter)
(Affine.Simplex.mongePointWeightsWithCircumcenter n)The Monge point of an (n+2)-simplex, in terms of
pointsWithCircumcenter.
- Defined in
- Mathlib.Geometry.Euclidean.MongePoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites53
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
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- Finset.cardproof · cited by 2,327
- Nat.cast_zeroproof · cited by 1,870
- HVAdd.hVAddproof · cited by 1,820
- MetricSpacestatement and proof · cited by 1,684
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Triangle.dist_orthocenter_reflection_circumcenterproof · cited by 3