Editing Euler line (section)

{{Short description|Line constructed from a triangle}}
[[Image:Triangle.EulerLine.svg|thumb|
{{legend-line|solid red|Euler's line, with [[Nine-point center|the center]] of the [[nine-point circle]]}}
{{legend-line|solid #D2691E|[[Median (geometry)|Medians]] (intersect at the [[centroid]])}}
{{legend-line|solid blue|[[Altitude (triangle)|Altitude]]s (intersect at the [[orthocenter]])}} 
{{legend-line|solid green|Perpendicular lines from the side midpoints (intersect at the [[circumcenter]])}}]]

In [[geometry]], the '''Euler line''', named after [[Leonhard Euler]] ({{IPAc-en|ˈ|ɔɪ|l|ər}} {{respell|OY|lər}}), is a [[line (mathematics)|line]] determined from any [[triangle]] that is not [[equilateral triangle|equilateral]]. It is a [[Central line (geometry)|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.<ref name="k">{{cite journal
 | author = Kimberling, Clark
 | title = Triangle centers and central triangles
 | journal = Congressus Numerantium
 | volume = 129
 | year = 1998
 | pages = i–xxv, 1–295}}</ref>

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