Theorems · Theorem · geometry

Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint

∀ {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) {i j : Fin (n + 1)},
  i ≠ j →
    ∀ {r : ℝ},
      r ∈ Set.Icc 0 1 →
        SignType.sign ((s.signedInfDist j) ((AffineMap.lineMap s.incenter (s.touchpoint ∅ i)) r)) =
          SignType.sign ((s.signedInfDist j) s.incenter)

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

0 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero