Ceva theorem
From Encyclopedia of Mathematics
A theorem on the relation between the lengths of certain lines intersecting a triangle. Let 
be three points lying, respectively, on the sides 
, 
and 
of a triangle 
. For the lines 
, 
and 
to intersect in a single point or to be all parallel it is necessary and sufficient that
 |
Lines 
, 
and 
that meet in a single point and pass through the vertices of a triangle are called Ceva, or Cevian, lines. Ceva's theorem is metrically dual to the Menelaus theorem. It is named after G. Ceva [1].
Ceva's theorem can be generalized to the case of a polygon. Let a point 
be given in a planar polygon with an odd number of vertices 
, and suppose that the lines 
intersect the sides of the polygon opposite to 
respectively in points 
, 
. In this case
 |
References
| [1] | G. Ceva, "De lineis rectis se invicem secantibus statica constructio" , Milano (1678) |
Comments
References
| [a1] | M. Berger, "Geometry" , I , Springer (1987) |
How to Cite This Entry:
Ceva theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ceva_theorem&oldid=33015
Ceva theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ceva_theorem&oldid=33015
This article was adapted from an original article by P.S. Modenov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article