Over the field with q elements the projective plane \(\mathbb{P}^2\) has
$$ q^2 + q + 1 $$
elements. It breaks up into:
-
A copy of \(\mathbb{F}_q^2\), with q2 elements.
-
A copy of \(\mathbb{F}_q^1\), with q elements.
-
A copy of \(\mathbb{F}_q^0\), with 1 element.
Higher-dimensional projective spaces follow the same pattern.
