Theorems · Definition · geometry

Affine.Simplex.eulerPoint

{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} → Affine.Simplex ℝ P n → Fin (n + 1) → P

Euler points are a set of points that the ninePointCircle passes through. They are defined as being $1/n$th of the way from the Monge point to a vertex. Specifically for triangles, these are the midpoints between the orthocenter and a given vertex (Affine.Triangle.eulerPoint_eq_midpoint).

Defined in

Mathlib.Geometry.Euclidean.NinePointCircle

Cited by

10 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor