7
Affine and Projective Planes
7.1 Affine planes
In what follows we will call the blocks of a PBD lines. If several points belong to the same line we will say that they are collinear, and if two lines fail to intersect we will say that they are parallel. Additionally, if the point p belongs to the line l we will say that p is on the line and that l passes through p
An affine plane is a PBD (P,B) with the following properties:
(1) P contains at least one subset of4 points no 3 ofwhich are collinear, and
(2) (parallel postulate) given a line l and a point p not on l , there is EXACTLY one line of B
Figure 7.1: Affine plane.
Remark Condition ...
Get Design Theory, 2nd Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
