Theorems · Theorem · geometry

Finset.centroid_def

∀ (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] {ι : Type u_4} (s : Finset ι) (p : ι → P),
  Finset.centroid k s p = (Finset.affineCombination k s p) (Finset.centroidWeights k s)

The definition of the centroid.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Centroid

Cited by

3 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsor