Meaning of Euler line | Babel Free

Definitions

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.
2. An Eulerian path, a looped path through a graph that passes along every edge exactly once.

Equivalents

Examples

“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.”

“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.”

“2011, Derek Allan Holton, A Second Step to Mathematical Olympiad Problems, World Scientific Publishing, Mathematical Olympiad Series, Volume 7, page 57, Show⟳ that the perpendicular bisector of LM in Figure⟳ 2.5 meets the Euler line halfway between the orthocentre and the circumcentre of ΔABC.”

“Theorem 2.1 A connected graph with even local degrees has an Euler line.”

“In defining an Euler graph, some authors drop the requirement that the Euler line be closed.”

“Euler lines mainly deal⟳ with the nature of connectivity in graphs. The concept of an Euler line is used to solve⟳ several puzzles and games.[…]A closed walk⟳ running through every edge of the graph G exactly once is called an Euler line.”

CEFR level