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Riemannian Geometry,New Chuck Norris Or Someone Whos Always TravelingIn His Classic Work Of Geometry, Euclid Focused On The Properties Of Flat Surfaces. In The Age Of Exploration, Mapmakers Such As Mercator Had To Concern Themselves With The Properties Of Spherical Surfaces. The Study Of Curved Surfaces, Or Noneuclidean Geometry, Flowered In The Late Nineteenth Century, As Mathematicians Such As Riemann Increasingly Questioned Euclid'S Parallel Postulate, And By Relaxing This Constraint Derived A Wealth Of New Results.