Theorems · Theorem · geometry

Affine.Simplex.excenterExists_singleton

∀ {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} [inst_4 : NeZero n] (s : Affine.Simplex ℝ P n) [n.AtLeastTwo]
  (i : Fin (n + 1)), s.ExcenterExists {i}

The existence of the excenter opposite a vertex (in two or more dimensions), expressed in terms of ExcenterExists.

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

13 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZeroNat.AtLeastTwo