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:
“No other creative field is as closed to those who are not white and male as is the visual arts. After I decided to be an artist, the first thing that I had to believe was that I, a black woman, could penetrate the art scene, and that, further, I could do so without sacrificing one iota of my blackness or my femaleness or my humanity.”
—Faith Ringgold (b. 1934)