Theorems · Definition · geometry

Affine.Simplex.altitudeFoot

{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 → Fin (n + 1) → P

The foot of an altitude is the orthogonal projection of a vertex of a simplex onto the opposite face.

Defined in

Mathlib.Geometry.Euclidean.Altitude

Cited by

23 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero