Stereographic Projection: Conformal Mapping from Sphere to Plane

① This example demonstrates the stereographic projection, a classic geometric transformation that maps points on a sphere (except the north pole) to a plane, showing the correspondence between the sphere and the plane. ② Core mathematical concepts include spherical geometry, projection transformation, conformal (angle-preserving) mapping, and the relationship between points and their images, including how latitude and longitude lines project to circles or lines on the plane. ③ Construction highlights: using GeoGebra commands such as Join, Sequence, Polygon, and Sphere to build the sphere, projection points, and the projection plane; objects include sphere f, point list L_1, line l, center O, radius R, points L, n, e, h, multiple lists (liste1, liste2, liste3, liste4), points A, B, C, D, polygon poly1, and images image1 and image2 to visualize the projection process. ④ Suitable for high school and university students in geometry courses, useful for understanding the Riemann sphere in complex analysis, map projection principles, and intuitive teaching of geometric transformations.