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The fashionable examine of space generalizes these ideas to include larger-dimensional geometry, non-Euclidean geometries (which play a central position in general relativity ) and topology Amount and house both play a task in analytic geometry , differential geometry , and algebraic geometry Convex and discrete geometry have been developed to resolve problems in quantity idea and purposeful evaluation however now are pursued with an eye fixed on functions in optimization and pc science Within differential geometry are the ideas of fiber bundles and calculus on manifolds , in particular, vector and tensor calculus Within algebraic geometry is the description of geometric objects as solution sets of polynomial equations, combining the concepts of amount …