Euler line
English edit
Alternative forms edit
Etymology edit
Named for Swiss mathematician Leonhard Euler.
Noun edit
Euler line (plural Euler lines)
- (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.
- 1983, The American Mathematical Monthly, volume 40, page 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.
- 2000, Alfred S. Posamentier, Making Geometry Come Alive: Student Activities and Teacher Notes[1], page 147:
- 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.
- (graph theory) An Eulerian path, a looped path through a graph that passes along every edge exactly once.
- 1961, Yale University, Graphs and Their Uses[2], page 25:
- Theorem 2.1 A connected graph with even local degrees has an Euler line.
- 2009, J. P. Chauhan, Krishna's Applied Discrete Mathematics[3], page 279:
- In defining an Euler graph, some authors drop the requirement that the Euler line be closed.
- 2013, Bhavanari Satyanarayana, Kuncham Syam Prasad, Near Rings, Fuzzy Ideals, and Graph Theory, page 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 edit
geometry
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graph theory