Riemann mapping theorem facts for kids

The Riemann mapping theorem says that for every region (without holes) on the [complex plane], there exists a smooth, angle-preserving, one-to-one map that takes our region to the unit disk. (The unit disk is the inside of the circle of radius 1 centered at the origin). This map is uniquely determined if you pick a point in your starting region to map to the origin, such that the derivative at that point is on the real line and strictly greater than zero.

See also

In Spanish: Teorema de representación conforme de Riemann para niños