Theorems · Definition · geometry

Affine.Simplex.exsphere

{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} → [NeZero n] → Affine.Simplex ℝ P n → Finset (Fin (n + 1)) → EuclideanGeometry.Sphere P

The exsphere with signs determined by the given set of indices (for the empty set, this is the insphere; for a singleton set, this is the exsphere opposite a vertex). This is only meaningful if s.ExcenterExists; otherwise, it is a sphere of radius zero at some arbitrary point.

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

20 results in Mathlib

Foundations

Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero