Example of conformal transformation.
In mathematics, conformal geometry is the study of conformed transformations (those that preserve angles) in a space. In two real dimensions, the conformal geometry is precisely the geometry of the Riemann surfaces. In more than two dimensions, conformal geometry can refer both to the study of conformal transformations in "flat" spaces (such as Euclidean spaces or spheres), or more commonly, to the study of conforming varieties that are varieties of Riemann equipped with a metric class defined in the absence of scale. The study of these structures is sometimes called Möbius geometry, and is a type of Klein geometry (a discipline named after the German mathematician Felix Klein).
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