Theorems · Theorem · geometry

Affine.Simplex.height_eq_dist

∀ {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] (s : Affine.Simplex ℝ P 1) (i : Fin 2), s.height i = dist (s.points 0) (s.points 1)

The height of a 1-dimensional simplex equals to the distance between the two vertices.

Defined in

Mathlib.Geometry.Euclidean.Altitude

Cited by

0 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor