Difference between revisions of "Euler straight line"
From Encyclopedia of Mathematics
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| − | The straight line passing through the point | + | {{TEX|done}} |
| + | 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). | This line was first considered by L. Euler (1765). | ||
Revision as of 20:18, 31 July 2014
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
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