Theorems · Theorem · geometry

Affine.Simplex.face_centroid_eq_centroid

∀ {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} (s : Affine.Simplex k P n) {fs : Finset (Fin (n + 1))} {m : ℕ} (h : fs.card = m + 1),
  Finset.centroid k Finset.univ (s.face h).points = Finset.centroid k fs s.points

The centroid of a face of a simplex as the centroid of a subset of the points.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid

Cited by

3 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsor