Theorems · Definition · geometry

Affine.Triangle.orthocenter

{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] → Affine.Triangle ℝ P → P

The orthocenter of a triangle is the intersection of its altitudes. It is defined here as the 2-dimensional case of the Monge point.

Defined in

Mathlib.Geometry.Euclidean.MongePoint

Cited by

23 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor