Geometry (from Ancient Greek: geo, "earth", and metria, "measure") is a branch of Mathematics dealing with issues related to shape, relative position and properties of figures in a given space. Geometry arose naturally and independently in several ancient cultures. During a long period of human history, Geometry was restricted to a single type — Euclidean Geometry —, presented in an axiomatized form in Euclid's Elements (\(\Sigma\tau o\iota\chi\varepsilon\tilde{\iota}\alpha\)), (about 3rd century B.C.), and its study was later extended (in the 19th century) with the introduction of alternative geometries, such as Hyperbolic Geometry and, more generally, Riemannian Geometry. Differential Geometry is an important branch of Mathematics where Analysis techniques are used in the study of the geometry of curves and surfaces.


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