Theorems · Theorem · geometry

Affine.Simplex.circumcenter_reindex

∀ {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] {m n : ℕ} (s : Affine.Simplex ℝ P m) (e : Fin (m + 1) ≃ Fin (n + 1)),
  (s.reindex e).circumcenter = s.circumcenter

Reindexing a simplex along an Equiv of index types does not change the circumcenter.

Defined in

Mathlib.Geometry.Euclidean.Circumcenter

Cited by

2 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor