Namespaces
Variants
Actions

Euler straight line

From Encyclopedia of Mathematics
Revision as of 20:18, 31 July 2014 by Ivan (talk | contribs) (TeX)
Jump to: navigation, search

The straight line passing through the point $H$ of intersection of the altitudes of a triangle, the point $S$ of intersection of its medians, 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

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=16830
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article