# A model of PG(2,3)

- Author:
- Zoltán Kovács

See also the Wikipedia page on projective planes.

## A very short introduction to PG(2,3)

The points in PG(2,3) are the sets {A

_{1},B_{1}}, {A_{2},B_{2}}, ..., {A_{13},B_{13}}. There are 13 points in PG(2,3). The lines can also be identified with sets {A_{1}',B_{1}'}, {A_{2}',B_{2}'}, ..., {A_{13}',B_{13}'}, they can be represented with the same 3D points (but the objects "in reality" differ). The vector B_{n}always equals to 2A_{n}where the coordinates are computed modulo 3. A point P represented with coordinates (x,y,z) and a line l represented with coordinates (a,b,c) are incident if x·a+y·b+z·c=0 (modulo 3). These assumptions lead to a matrix M that contains all lines, in each row the points of a certain line are given, in PG(2,3). For example, {A_{2},B_{2}}, {A_{5},B_{5}}, {A_{8},B_{8}}, {A_{11},B_{11}} are collinear points of PG(2,3) on a line in PG(2,3).