Projective Plan

The concept of projective plan has two distinct directions, which is recut.

Algebraic geometry

A projective plane in algebraic geometry is a variety, so called projective Espace of dimension 2. One can associate a projective plan with each following body: the real numbers, the complex numbers, the Quaternion S and the Octonion S.

Combinative geometry

In combinative geometry, a projective plane of order N is a whole of points and lines (i.e. of groupings of points that one will call right-hand sides) such as:

There is $n^2+n+1$ points and as many lines.

Each right has $n+1$ points and each point belongs to $n+1$ right exactly.

Two distinct lines meet in only one point.

Two not S distinct meets in only one line.

One can build such objects by taking the points in a Corps finished of the projective plan within the meaning of the algebraic geometry. Number N is then a power of a Prime number.

Projective axioms and plans

One considers generally various levels in the Axiomes of projective plans, or PP: the PP of incidence, PP de Pappus, PP de Désargues, etc

Random links: