Theorems · Definition · geometry

Affine.Simplex.excenter

{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)) → P

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

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

63 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero