Difference between revisions of "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 | + | |
| + | The straight line passing through the point $H$ of intersection of the altitudes of a triangle, the point $S$ of intersection of its [[Median (of a triangle)|median]]s (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 | ||
$$OH:SH=1:2$$ | $$OH:SH=1:2$$ | ||
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====Comments==== | ====Comments==== | ||
| − | + | See also: [[Triangle centre]] | |
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)</TD></TR></table> | ||
Latest revision as of 20:16, 16 January 2016
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=32621
Euler straight line. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_straight_line&oldid=32621
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article