Euler line

English right|thumb|The Euler line (e) of a triangle, passing through the orthocentre (H), centroid (S), circumcentre (U) and the nine-point centre (N) Alternative forms en Euler's line Etymology Named for Swiss mathematician Leonhard Euler. Noun en geometry 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. en 1983 The American Mathematical Monthly 40 https://books.google.com.au/books?id=Q8c0AAAAIAAJ&q=%22Euler+line%22%7C%22Euler+lines%22&dq=%22Euler+line%22%7C%22Euler+lines%22&hl=en&sa=X&ved=0ahUKEwiwrNnTnffNAhVLEpQKHeHBBIUQ6AEIjwIwKg 199 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. en 2000 Alfred S. Posamentier Making Geometry Come Alive: Student Activities and Teacher Notes 147 https://books.google.com.au/books?id=B4HPFu_-uaIC&pg=PA147&dq=%22Euler+line%22%7C%22Euler+lines%22&hl=en&sa=X&ved=0ahUKEwiwrNnTnffNAhVLEpQKHeHBBIUQ6AEItQEwGg#v=onepage&q=%22Euler%20line%22%7C%22Euler%20lines%22&f=false 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 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. en graph theory An Eulerian path, a looped path through a graph that passes along every edge exactly once. en 1961 Yale University Graphs and Their Uses 25 https://books.google.com.au/books?id=9KUNAQAAIAAJ&q=%22Euler+line%22%7C%22Euler+lines%22&dq=%22Euler+line%22%7C%22Euler+lines%22&hl=en&sa=X&ved=0ahUKEwiwrNnTnffNAhVLEpQKHeHBBIUQ6AEIvQIwNA Theorem 2.1 A connected graph with even local degrees has an Euler line. en 2009 J. P. Chauhan Krishna's Applied Discrete Mathematics 279 https://books.google.com.au/books?id=DeRCEDw8emgC&pg=PA279&dq=%22Euler+line%22%7C%22Euler+lines%22&hl=en&sa=X&ved=0ahUKEwiwrNnTnffNAhVLEpQKHeHBBIUQ6AEI3wIwPA#v=onepage&q=%22Euler%20line%22%7C%22Euler%20lines%22&f=false In defining an Euler graph, some authors drop the requirement that the Euler line be closed. en 2013 Bhavanari Satyanarayana; Kuncham Syam Prasad Near Rings, Fuzzy Ideals, and Graph Theory https://books.google.com.au/books?id=gzHOBQAAQBAJ&pg=PA372&dq=%22Euler+line%22%7C%22Euler+lines%22&hl=en&sa=X&ved=0ahUKEwiwrNnTnffNAhVLEpQKHeHBBIUQ6AEIyQEwHQ#v=onepage&q=%22Euler%20line%22%7C%22Euler%20lines%22&f=false 372 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. Translations geometry Hungarian: hu Euler-egyenes graph theory See also en Hamiltonian path en eponyms