Riemann Sphere: Complex Number Geometry

Draw a geometric model combining a unit sphere and the complex plane. Points on the complex plane represent complex numbers, and the unit sphere intersects the plane to form a sphere. Points on the sphere are connected to points on the plane via intersection lines. Construct by first drawing the complex plane and the unit sphere, then finding their intersection points, connecting these points to sphere points, and finally drawing circles centered at plane points with radius equal to the sphere's radius. This model illustrates the relationship between complex numbers and geometry, suitable for high school or college students learning analytic geometry and complex numbers.