Euler straight line
From Encyclopedia of Mathematics
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 straight line. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_straight_line&oldid=37564
Euler straight line. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_straight_line&oldid=37564
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article