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"measurement") is, with arithmetic, one of the oldest branches of mathematics.

It is concerned with properties of space that are related with distance, shape,

size, and relative position of figures. A mathematician who works in the

field of geometry is called a geometer.

Until the 19th century, geometry was almost exclusively devoted to Euclidean

geometry, which includes the notions of point, line, plane, distance, angle,

surface, and curve, as fundamental concepts.

During the 19th century several discoveries enlarged dramatically the scope

of geometry. One of the oldest such discoveries is Gauss' Theorema Egregium

(remarkable theorem) that asserts roughly that the Gaussian curvature of a

surface is independent from any specific embedding in an Euclidean space.

This implies that surfaces can be studied intrinsically, that is as stand alone

spaces, and has been expanded into the theory of manifolds and

Riemannian geometry.

Later in the 19th century, it appeared that geometries without the parallel

postulate (non-Euclidean geometries) can be developed

without introducing any contradiction. The geometry that

underlies general relativity is a famous application of

non-Euclidean geometry.