Theorems · Theorem · geometry

centroid_mem_affineSpan_of_card_eq_add_one

∀ (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} [CharZero k] {s : Finset ι} (p : ι → P) {n : ℕ},
  s.card = n + 1 → Finset.centroid k s p ∈ affineSpan k (Set.range p)

In the characteristic zero case, the centroid lies in the affine span if the number of points is n + 1.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Centroid

Cited by

3 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorCharZero