Theorems · Theorem · geometry

Affine.Simplex.faceOppositeCentroid_mem_affineSpan_face

∀ {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] {n : ℕ} [inst_4 : NeZero n] [CharZero k] (s : Affine.Simplex k P n) (i : Fin (n + 1)),
  s.faceOppositeCentroid i ∈ affineSpan k (Set.range (s.faceOpposite i).points)

The centroid of the face opposite a vertex lies in the affine span of that face.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid

Cited by

2 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorNeZeroCharZero