In
geometry a striking feature of
projective planes is the
symmetry of the roles played by
points and
lines in the definitions and theorems, and (
plane)
duality is the formalization of this concept. There are two approaches to the subject of duality, one through language and the other a more functional approach through special
mappings. These are completely equivalent and either treatment has as its starting point the
axiomatic version of the geometries under consideration. In the functional approach there is a map between related geometries that is called a
duality. Such a map can be constructed in many ways. The concept of plane duality readily extends to space duality and beyond that to duality in any finite-dimensional
projective geometry.