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File:Riemann sphere1.svg
Stereographic projection is a conformal equivalence between a portion of the sphere (with its standard metric) and the plane with the metric <math> \frac{4}{(1 + X^2 + Y^2)^2} \; ( dX^2 + dY^2)</math>.
In mathematics and theoretical physics, two geometries are conformally equivalent if there exists a conformal transformation (an angle-preserving transformation) that maps one geometry to the other one.<ref>Template:Citation.</ref> More generally, two Riemannian metrics on a manifold M are conformally equivalent if one is obtained from the other by multiplication by a positive function on M.<ref>Template:Citation.</ref> Conformal equivalence is an equivalence relation on geometries or on Riemannian metrics.