Euler line

  Euler's line, with the center of the nine-point circle
  Medians (intersect at the centroid)
  Altitudes (intersect at the orthocenter)
  Perpendicular lines from the side midpoints (intersect at the circumcenter)

In geometry, the Euler line, named after Leonhard Euler (/ˈɔɪlər/), is a line determined from any triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle.[1]

The concept of a triangle's Euler line extends to the Euler line of other shapes, such as the quadrilateral and the tetrahedron.

  1. ^ Kimberling, Clark (1998). "Triangle centers and central triangles". Congressus Numerantium. 129: i–xxv, 1–295.