Theorems · Theorem · geometry

Affine.Triangle.altitude_eq_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] (t : Affine.Triangle ℝ P) {i₁ i₂ i₃ : Fin 3},
  i₁ ≠ i₂ → i₁ ≠ i₃ → i₂ ≠ i₃ → Affine.Simplex.altitude t i₁ = Affine.Simplex.mongePlane t i₂ i₃

In the case of a triangle, altitudes are the same thing as Monge planes.

Defined in

Mathlib.Geometry.Euclidean.MongePoint

Cited by

2 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor