Affine.Simplex.centroid_mem_affineSpan
∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[inst_3 : AddTorsor V P] [CharZero k] {n : ℕ} (s : Affine.Simplex k P n),
s.centroid ∈ affineSpan k (Set.range s.points)The centroid lines in the affine span of the simplex's vertices.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.rangestatement · cited by 4,705
- AddTorsorstatement and proof · cited by 1,657
- DivisionRingstatement and proof · cited by 1,062
- CharZerostatement and proof · cited by 932
- AffineSubspacestatement · cited by 871
- Affine.Simplexstatement and proof · cited by 471
- affineSpanstatement · cited by 417
- Affine.Simplex.pointsstatement and proof · cited by 391
- Affine.Simplex.centroidstatement · cited by 39
- Finset.card_finproof · cited by 26
Cited by2
Results whose statement or proof uses this declaration.
- Affine.Simplex.faceOppositeCentroid_mem_affineSpan_faceproof · cited by 2
- Affine.Simplex.ninePointCircle_center_mem_affineSpanproof · cited by 2