Theorems · Theorem · geometry

EuclideanGeometry.exists_circumcenter_eq_of_cospherical_subset

∀ {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] {s : AffineSubspace ℝ P} {ps : Set P},
  ps ⊆ ↑s →
    ∀ [Nonempty ↥s] {n : ℕ} [FiniteDimensional ℝ ↥s.direction],
      Module.finrank ℝ ↥s.direction = n →
        EuclideanGeometry.Cospherical ps →
          ∃ c, ∀ (sx : Affine.Simplex ℝ P n), Set.range sx.points ⊆ ps → sx.circumcenter = c

All n-simplices among cospherical points in an n-dimensional subspace have the same circumcenter.

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

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNonemptyFiniteDimensional