Theorems · Theorem · geometry

Affine.Simplex.collinear_point_centroid_faceOppositeCentroid

∀ (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] [CharZero k] {n : ℕ} [inst_5 : NeZero n] (s : Affine.Simplex k P n) (i : Fin (n + 1)),
  Collinear k {s.points i, s.centroid, s.faceOppositeCentroid i}

For a simplex, the centroid, a vertex, and the corresponding faceOppositeCentroid are collinear.

Defined in

Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

Cited by

0 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddTorsorCharZeroNeZero