. A two dimensional example of an open geometry is the surface of a saddle, represented below.
A flat geometry is the familiar Euclidean geometry, in which a circle has a circumference equal to.
A closed geometry has "less space" than the familiar flat geometry. In this geometry a circle has a circumference less than. A two dimensional example of a closed geometry is the surface of a sphere (like the earth!)
These images were taken from Ned Wright's cosmology tutorial.