Projective Planes
A projective plane is a type of geometric structure that extends the concept of a plane in a way that allows for the inclusion of "points at infinity." In a projective plane, any two lines intersect at exactly one point, and any two points lie on exactly one line. This property helps eliminate parallel lines, making it a useful concept in various fields of mathematics.
Projective planes can be constructed using finite fields, leading to the creation of finite projective planes. One famous example is the Fano Plane, which is the smallest projective plane, consisting of seven points and seven lines. Projective geometry has applications in areas such as computer graphics, coding theory, and the study of perspective in art.