Difference between revisions of "Median (of a triangle)"
From Encyclopedia of Mathematics
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| − | A straight line (or its segment contained in the triangle) which joins a vertex of the triangle with the midpoint of the opposite side. The three medians of a triangle intersect at one point, called the centre of gravity, the centroid or the barycentre of the triangle. This point divides each median into two parts with ratio | + | {{TEX|done}} |
| + | A straight line (or its segment contained in the triangle) which joins a vertex of the triangle with the midpoint of the opposite side. The three medians of a triangle intersect at one point, called the centre of gravity, the centroid or the barycentre of the triangle. This point divides each median into two parts with ratio $2:1$ if the first segment is the one that starts at the vertex. | ||
Revision as of 16:05, 9 April 2014
A straight line (or its segment contained in the triangle) which joins a vertex of the triangle with the midpoint of the opposite side. The three medians of a triangle intersect at one point, called the centre of gravity, the centroid or the barycentre of the triangle. This point divides each median into two parts with ratio $2:1$ if the first segment is the one that starts at the vertex.
Comments
J. Hjelmslev has shown that also in hyperbolic geometry (cf. Lobachevskii geometry) the meridians of a triangle intersect at a point.
References
| [a1] | H.S.M. Coxeter, "Introduction to geometry" , Wiley (1989) |
How to Cite This Entry:
Median (of a triangle). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Median_(of_a_triangle)&oldid=15602
Median (of a triangle). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Median_(of_a_triangle)&oldid=15602
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article