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Condensed from http://en.wikipedia.org/wiki/Geometry
Geometry is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Euclid's axiomatic treatment  Euclidean geometry  is perhaps one of the best known works.
Descartes introduced coordinates, and along with algebra allowed an analytical treatment incorporating functions and equations. This played a key role in the emergence of calculus in the 17th century. The theory of perspective showed that there is more to geometry than just the metric properties of figures. Following that line, Euler and Gauss broke free of the specific notion of distance, which led to the creation of topology and differential geometry.
The discovery of nonEuclidean geometry led to new ways of thinking about space, and modern geometry considers manifolds, which are objects that are locally similar to the usual Euclidean space, but may differ on a larger scale.
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