Theorems · Theorem · geometry

Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {n : ℕ} (s : Affine.Simplex ℝ P n) (fs : Finset (Fin (n + 1))),
  Finset.centroid ℝ fs s.points =
    (Finset.affineCombination ℝ Finset.univ s.pointsWithCircumcenter)
      (Affine.Simplex.centroidWeightsWithCircumcenter fs)

The centroid of some vertices of a simplex, in terms of pointsWithCircumcenter.

Defined in

Mathlib.Geometry.Euclidean.Circumcenter

Cited by

3 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor