# Duality (projective Geometry)

Duality (projective 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 metamathematical concept. There are two approaches to the subject of duality, one through language (the Principle of Duality) and the other a more functional approach. 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 which is called a duality. In specific examples, 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.

### Other articles related to "duality":

Duality (projective Geometry) - Preservation of Incidence
... The dualitymapping g is an isomorphism with respect to the incidence properties such as collinearity and concurrency) ... this property given a pair of lines L1 and L2 which intersect at a point P,then their dual points gL1 and gL2 define the unique line gâ’1P ... points P1 and P2 through which passes line L,P1.P2 L,then what is the intersection of lines gâ’1P1 and gâ’1P2?If gâ’1P1 ˆ’1P2 P then so that â´Given a ...