Theorems · Theorem · geometry

Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero

∀ {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 j : Fin (n + 1)} (h : i ≠ j),
  have this := ⋯;
  inner ℝ (s.points j -ᵥ s.altitudeFoot i) (s.points i -ᵥ s.altitudeFoot i) = 0

Altitudes are perpendicular to the faces containing their foot.

Defined in

Mathlib.Geometry.Euclidean.Altitude

Cited by

1 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor