Space

A space is a continuum of points. The dimensionality of a space is the amount of coordinates required to specify the location of a point (excluding spacefilling curves and the like). Spaces can be embedded in higher-dimensional spaces. For example, in 3-dimensional space, a plane is an embedding of 2-dimensional euclidean space while a sphere is an embedding of 2-dimension spherical space.

Curvature
Spaces can be divided into three categories based on curvature: spherical, euclidean and hyperbolic.


 * Spherical - positive curvature; the circumfrence of a circle < πr2; a2+b2>c2 if a, b and c are the sides of a right triangle; finite
 * Euclidean - zero curvature; the circumfrence of a circle = πr2; a2+b2=c2 if a, b and c are the sides of a right triangle; infinite
 * Hyperbolic - zero curvature; the circumfrence of a circle > πr2; a2+b2<c2 if a, b and c are the sides of a right triangle; infinite