Theorems · Theorem · geometry

Affine.Simplex.vectorSpan_isOrtho_altitude_direction

∀ {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} (s : Affine.Simplex ℝ P n) (i : Fin (n + 1)),
  vectorSpan ℝ (s.points '' {i}ᶜ) ⟂ (s.altitude i).direction

The vector span of the opposite face lies in the direction orthogonal to an altitude.

Defined in

Mathlib.Geometry.Euclidean.Altitude

Cited by

2 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor