Theorems · Theorem · geometry

Affine.Simplex.centroid_notMem_affineSpan_of_ne_univ

∀ {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} [CharZero k] (s : Affine.Simplex k P n) {t : Set (Fin (n + 1))},
  t ≠ Set.univ → s.centroid ∉ affineSpan k (s.points '' t)

The centroid of a simplex does not lie in the affine span of any proper subset of its vertices.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorCharZero