Quadrangle, complete

From Encyclopedia of Mathematics
Revision as of 17:19, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A collection of four points (lying in a plane), no three of which lie on the same line, and the six lines connecting these points (cf. Fig.).

Figure: q076010a

The points are called the vertices, and the lines are called the edges of the complete quadrangle. Edges that have no common vertex are called opposite; the points of intersection of the opposite edges are called diagonal points.

If and are the points of intersection of the line with the lines and , then the four points form a harmonic quadruple of points. The dual figure to a quadrangle is called a quadrilateral — a collection of four lines (in a plane), no three of which contain a common point.



[a1] H.S.M. Coxeter, "Projective geometry" , Springer (1987) pp. 7; 95
[a2] H.S.M. Coxeter, "Introduction to geometry" , Wiley (1963)
[a3] M. Berger, "Geometry" , 1–2 , Springer (1987) (Translated from French)
How to Cite This Entry:
Quadrangle, complete. Encyclopedia of Mathematics. URL:,_complete&oldid=17067
This article was adapted from an original article by P.S. ModenovA.S. Parkhomenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article