Theorems · Definition · geometry

Affine.Simplex.mongePlane

{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} → Affine.Simplex ℝ P (n + 2) → Fin (n + 3) → Fin (n + 3) → AffineSubspace ℝ P

A Monge plane of an (n+2)-simplex is the (n+1)-dimensional affine subspace of the subspace spanned by the simplex that passes through the centroid of an n-dimensional face and is orthogonal to the opposite edge (in 2 dimensions, this is the same as an altitude). This definition is only intended to be used when i₁ ≠ i₂.

Defined in

Mathlib.Geometry.Euclidean.MongePoint

Cited by

8 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor