Theorems · Theorem · geometry

Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face

∀ {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} {signs : Finset (Fin (n + 1))},
  s.ExcenterExists signs →
    ∀ {fs : Finset (Fin (n + 1))} {m : ℕ} (hfs : fs.card = m + 1),
      m ≠ n → s.excenter signs ∉ affineSpan ℝ (Set.range (s.face hfs).points)

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

4 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero