Riemann Number Sphere: Stereographic Projection of Complex Numbers

① This example demonstrates the construction of the Riemann sphere, mapping points from the complex plane onto a unit sphere via stereographic projection, illustrating the one-to-one correspondence between complex numbers and points on the sphere. ② Core mathematical concepts include the extended complex plane, stereographic projection, the point at infinity, and geometric transformations on the sphere; it also involves basic geometric elements such as spheres and line segments. ③ Construction highlights: using GeoGebra's Sphere command to create the unit sphere, Segment command to draw the projection line from the north pole to a complex plane point, with objects including sphere center S, north pole N, complex plane point C, sphere projection point Z, function f, and the Equator; dynamically adjusting the complex point reveals the projection changes. ④ Suitable for high school to university-level teaching of complex numbers, introductory complex analysis, or geometric visualization courses, helping students understand the representation of complex numbers on a sphere and the concept of infinity.