The Euler line (“oiler”) is the line that passes through the orthocenter, circumcenter, and centroid. The orthocenter is the point at which the three altitudes of the triangle intersect. The circumcenter is the point at which all the perpendicular bisectors intersect. Lastly, the centroid is the point at which the medians intersect.
The Euler line came about in the 18th century when the Swiss mathematician, Leonhard Euler, discovered the property that the orthocenter, circumcenter, and centroid all have. He observed that they all are collinear. The distance from the orthocenter to the centroid is twice the distance from the circumcenter to the centroid, unless it is in an equilateral triangle and all these points lie in the same place.