Dynamic Curve Formed by Intersection of a Surface and a Moving Plane

This example demonstrates how the intersection curve between a 3D surface and a moving plane changes dynamically as the plane's position varies. The core mathematical concepts involve spatial analytic geometry, including surface equations, plane equations, and the computation of intersection curves between two surfaces, along with parametric curves and dynamic geometry principles. The construction uses GeoGebra commands such as Plane to define reference planes, Sequence to generate a series of moving planes, and IntersectPath to compute the intersection path for each plane with the given surface. The object list includes multiple points (A, B, C, D), planes (plane1, plane2, plane3), curves (c1, c2, c, d), surfaces (s1, s2), and sliders (r1, r2), allowing users to adjust parameters and observe the evolution of the intersection curve. This is suitable for high school or early university students to understand spatial curves and surfaces, and serves as an interactive teaching tool or mathematical experiment.