Part IV · Planes from fields · Lesson 11

Coordinates for a projective plane

PG(2, q): points and lines as subspaces of GF(q)³.

This lesson is planned. Here is what it will cover.

You’ll learn

• Points are the 1-dimensional subspaces of $\mathrm{GF}(q)^3$, written $[x : y : z]$; lines are the 2-dimensional subspaces.
• Counting gives $q^2 + q + 1$ points and $q + 1$ points per line.
• $\mathrm{PG}(2, 2)$ is the Fano plane; $\mathrm{PG}(2, 3)$ has 13 points.