Open, Flat, Closed
An isotropic and homogeneous space can be described by the metric:
- .
In the limit that the constant of curvature becomes infinitely large, a flat, Euclidean space is returned. It is essentially the same as setting to zero. If is not zero the space is not Euclidean. When the space is said to be closed or elliptic. When the space is said to be open or hyperbolic.
Triangles which lie on the surface of an open space will have a sum of angles which is less than 180°. Triangles which lie on the surface of a closed space will have a sum of angles which is greater than 180°. The volume, however, is not .
Read more about this topic: Curved Space
Famous quotes containing the word closed:
“Thus piteously Love closed what he begat:
The union of this ever-diverse pair!
These two were rapid falcons in a snare,
Condemned to do the flitting of the bat.”
—George Meredith (1828–1909)