Theorems · Theorem · geometry

Affine.Simplex.orthogonalProjection_circumcenter

∀ {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))} {m : ℕ}
  (h : fs.card = m + 1), ↑((s.face h).orthogonalProjectionSpan s.circumcenter) = (s.face h).circumcenter

The orthogonal projection of the circumcenter onto a face is the circumcenter of that face.

Defined in

Mathlib.Geometry.Euclidean.Circumcenter

Cited by

1 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor