# Euler straight line

From Encyclopedia of Mathematics

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The straight line passing through the point $H$ of intersection of the altitudes of a triangle, the point $S$ of intersection of its medians (the centroid), and the centre $O$ of the circle circumscribed to it. If the Euler line passes through a vertex of the triangle, then the triangle is either isosceles or right-angled, or both right-angled and isosceles. The segments of the Euler line satisfy the relation

$$OH:SH=1:2$$

This line was first considered by L. Euler (1765).

#### Comments

See also: Triangle centre

#### References

[a1] | H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963) |

**How to Cite This Entry:**

Euler line.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Euler_line&oldid=39654