5
votes
0answers
130 views

Existence of a special set of q+2 points in the finite affine plane over $\mathbb F_q$

I am working in the finite affine plane over $\mathbb F_q$ with $q=2^n$. Such a plane has $q^2$ points, $q^2+q$ lines, each line has $q$ points, and by a point is passing $q+1$ lines. There are $q+1$ ...
2
votes
1answer
311 views

Turning affine planes into projective planes

How can we show that an affine plane of order $n$ can always be turned into a projective plane of order $n$? Say I start with an affine plane, and split it into $n+1$ parallel classes, add a point ...
2
votes
3answers
97 views

Count points and lines in $\mathbb{A}^2(\mathbb{F}_p)$

Let $p$ be a prime, then $\mathbb{F}_p$ is a finite field. $\mathbb{A}^2(\mathbb{F}_p)$ is an affine plane. Number of points in $\mathbb{A}^2(\mathbb{F}_p)$ is $p^2$. I look at a line equation ...