In the 18th century, the Swiss mathematician Leonhard Euler noticed that three of the many centers of a triangle are always collinear, that is, they always lie on a straight line. This line has come to be named after him – the Euler line. The three centers that have this surprising property are the triangle’s centroid , circumcenter and orthocenter.
In the figure, the centroid is the black middle point on the line. The centroid is the point where the three medians converge.
The circumcenter is the purple point. The circumcenter is the point where the perpendicular bisectors of the triangle’s sides converge.
The orthocenter is the red point. The orthocenter is the point where the three altitudes of the triangle converge.
The Euler Line
