Theorems · Theorem · geometry

EuclideanGeometry.exists_circumradius_eq_of_cospherical

∀ {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] {ps : Set P} {n : ℕ} [FiniteDimensional ℝ V],
  Module.finrank ℝ V = n →
    EuclideanGeometry.Cospherical ps →
      ∃ r, ∀ (sx : Affine.Simplex ℝ P n), Set.range sx.points ⊆ ps → sx.circumradius = r

All n-simplices among cospherical points in n-space have the same circumradius.

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

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorFiniteDimensional