The modern study of space generalizes these ideas to include higher-dimensional

*geometry*, non-Euclidean*geometries*(which play a central role in general relativity) and topology. Quantity and space both play a role in analytic*geometry*, differential*geometry*, and algebraic*geometry*. Convex and discrete*geometry*were developed to solve problems in number theory and functional analysis but now are pursued with an eye on applications in optimization and computer science. Within differential*geometry*are the concepts of fiber bundles and calculus on manifolds, in particular, vector and tensor calculus.