Theorems · Theorem · geometry

Affine.Simplex.ExcenterExists.sum_excenterWeights_eq_one

∀ {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} [inst_4 : NeZero n] (s : Affine.Simplex ℝ P n) {signs : Finset (Fin (n + 1))},
  s.ExcenterExists signs → ∑ i, s.excenterWeights signs i = 1

Alias of the reverse direction of Affine.Simplex.sum_excenterWeights_eq_one_iff.

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

11 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero