Riemann Sphere

The Riemann sphere completes the complex plane by adding a single point at infinity, then wrapping the whole thing onto a sphere via stereographic projection. Every point on the plane maps to a unique point on the sphere, circles map to circles, and Möbius transformations become smooth rotations. Click on the plane to place points and watch them appear on the sphere. Apply Möbius transformations to see how they warp the plane while moving gracefully on the sphere.