Theorems · Theorem · geometry

Affine.Simplex.centroid_vsub_eq

∀ {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) (p : P),
  s.centroid -ᵥ p = (↑n + 1)⁻¹ • ∑ x, (s.points x -ᵥ p)

The vector from any point to the centroid is the average of vectors to the simplex vertices.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid

Cited by

4 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorCharZero