Quadrangle, complete
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 A,B,C,D are called the vertices, and the lines AB,CD,AC,BD,BC,AD are called the edges of the complete quadrangle. Edges that have no common vertex are called opposite; the points P,Q,R of intersection of the opposite edges are called diagonal points.
If S and T are the points of intersection of the line PQ with the lines AD and BC, then the four points P,Q,S,T 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.
References
[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) |
Quadrangle, complete. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quadrangle,_complete&oldid=53686