Projective plane with a finite number of points

A projective plane with a finite number of points is a special kind of geometry where every pair of points determines a unique line, and every pair of lines meets at a unique point. Unlike the usual plane, it has only a finite set of points and lines. The most common example is the projective plane over a finite field, often called a finite projective plane.

Important properties

• Any two distinct points determine exactly one line.

• Any two distinct lines meet at exactly one point.

• There are no parallel lines; all lines intersect.

• There is a constant number $n+1$ of points on each line and lines through each point, where $n$ is called the order of the plane.

• The total number of points and lines is $n^2 + n + 1$.