Intersection Curves of a Sphere and a Quadric: Curves on the Riemann Sphere

① This example demonstrates the spatial intersection curves formed when the Riemann sphere (stereographic projection of the complex plane) meets an arbitrary second quadric surface, visualizing the geometric shape of two surfaces intersecting in 3D. ② Core mathematical concepts include intersection of a sphere and a quadric, the Riemann sphere representation of complex numbers, parameterization of space curves, and symmetry analysis. ③ Construction highlights: uses GeoGebra's Intersect command to compute surface intersections, Sphere to construct the sphere, Point and Axes to set up the coordinate system, and multiple sliders (e.g., a, λ, b) to dynamically adjust quadric coefficients and observe curve changes; the object list includes many parameters (a_{11}, etc.) and text labels for real-time display of equations and values. ④ Suitable for high school to university courses in analytic geometry, complex analysis, or computer-aided geometry, serving as an interactive teaching tool to help students understand surface intersections and complex geometric meanings.