Riemann Sphere: Stereographic Projection from Complex Plane to Sphere

This example demonstrates the Riemann sphere, a fundamental geometric model in complex analysis, by establishing a one-to-one correspondence between points on the complex plane and points on a unit sphere, visually showing how the point at infinity maps to the north pole. The core mathematical concepts include stereographic projection of complex numbers, the extended complex plane, the point at infinity, and the correspondence between spherical and planar geometry. In terms of construction, the summary lists GeoGebra commands such as Point, Intersect, Sphere, Segment, Radius, and Circle, with objects including g, f, A, B, a, C, D, E, b, F, G, d, e, c, text1, animate, button1, h, K, and E', incorporating animation buttons and text labels to dynamically illustrate the projection process. This example is suitable for university-level mathematics students or advanced undergraduates studying complex analysis, topology, or geometry, and serves as a valuable classroom demonstration tool for teachers to help students grasp the topological equivalence between the complex plane and the sphere.