User:UnpleasantPheasant/sandbox

In geometry, a polar space is an incidence structure of points and lines which satisfies the following axioms:


 * There are at least three points on any line.
 * No line is collinear with every other point.
 * Find a nice way to say "finite Witt index". Remember that you want to include the infinite case.
 * Let p be a point not on a line l. Then p is collinear with either one point on l or every point on l.

A polar space of rank 2 is a generalized quadrangle. Polar spaces with a finite number of points and lines are also studied as combinatorial objects, and are a geometric interpretation of the classical groups.

Projective spaces
The main article doesn't cover this stuff. Eep.

Focus on finite? Nah, go all out, I say. Should I broaden it to anti-automorphisms and division rings, then?

Formed vector spaces
Alternating bilinear Hermitian (up to a scalar) Symmetric bilinear

Quadratics.