Some further information about non-Euclidean geometry:

Our handout on the parallel postulate and logic.

A few other statements equivalent to the Parallel Postulate:

- The Pythagorean Theorem
- The sum of the interior angles of a triangle is equal to the sum of two right angles
- There exists a triangle whose interior angles sum to the sum of two right angles
- Any three noncollinear points lie on a circle
- If three angles of a quadrilateral are right angles, so is the fourth

Spherical geometry:

brief overview

longer treatment

Hyperbolic geometry:

introduction ("neutral geometry" means the first four postulates)

one of the most common visualizations

Escher pictures that are hyperbolic:
one
two

miscellaneous hyperbolic geometry links