Projective Geometry

Eric Bainville - Oct 2007

The principle of duality

In projective geometry, all statements involving points, lines, and planes will remain valid when we swap "point" and "plane", and adjust the statement accordingly, for example "point on line" becomes "plane containing line"; "line by two points" becomes "line intersection of two planes", etc.

This principle is called duality. Since it is verified by the definitions of the objects, it extends naturally to all statements. I introduce it right now, so the reader can see the application of the principle in the definition of lines. I grouped all definitions and properties in pairs of dual statements.