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 $2:1$ if the first segment is the one that starts at the vertex. The centroid lies on the [[Euler straight line|Euler line]]. | 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. The centroid lies on the [[Euler straight line|Euler line]]. | ||
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====Comments==== | ====Comments==== | ||
| − | J. Hjelmslev has shown that also in hyperbolic geometry (cf. [[Lobachevskii geometry]]) the meridians of a triangle intersect at a point. | + | J. Hjelmslev has shown that also in [[hyperbolic geometry]] (cf. [[Lobachevskii geometry]]) the meridians of a triangle intersect at a point. |
====References==== | ====References==== | ||
<table> | <table> | ||
| − | <TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, | + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, "Introduction to geometry" , Wiley (1989) |
</TD></TR></table> | </TD></TR></table> | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Latest revision as of 14:54, 2 May 2023
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. The centroid lies on the Euler line.
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=37563
Median (of a triangle). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Median_(of_a_triangle)&oldid=37563
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article