In complex analysis, a conformal map is a function f : U > C (where U is an open subset of the complex numbers C) which maintains angles, and therefore the shape of small figures. A function f is conformal if and only if it is holomorphic and its derivative is everywhere nonzero.
(In other words, "conformal" means the almost same thing in cartography that it means in complex analysis.)
An important statement about conformal maps is the Riemann mapping theorem.
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