Euler line

Noun

Euler line (plural Euler lines)

1. A line that, for a given triangle, passes through several important points, including the circumcentre, orthocentre and centroid; an analogous line for certain other 2- and 3-dimensional geometric figures.
   • Since the line joining the circumcenter and orthocenter of a triangle is its Euler line, we see that this parabola is the envelope of the Euler lines of the triangles Aᵢ.1983, The American Mathematical Monthly, volume 40, page 199
   • The Euler line in the preceding figure is OH. N, the center of the nine-point circle, not only lies on the Euler line, but is also its midpoint.2000, Alfred S. Posamentier, Making Geometry Come Alive: Student Activities and Teacher Notes, page 147
2. An Eulerian path, a looped path through a graph that passes along every edge exactly once.
   • Theorem 2.1 A connected graph with even local degrees has an Euler line.1961, Yale University, Graphs and Their Uses, page 25
   • In defining an Euler graph, some authors drop the requirement that the Euler line be closed.2009, J. P. Chauhan, Krishna's Applied Discrete Mathematics, page 279