Incidence geometry

Summary

Incidence geometry is the part of geometry that studies points, lines and the relation "lies on", and nothing else. Its objects are incidence structures that satisfy axioms such as "two points lie on exactly one line". Affine planes, projective planes and finite geometries are its main examples. It asks which configurations the axioms force. It also asks which algebra, such as a field or a division ring, can be rebuilt from the points and lines alone.