Slicing a Cone: Dynamic Cross-Sections and Geometric Exploration

This example demonstrates how to dynamically generate cross-sections of a cone by rotating a cutting plane, visually showing how the intersection shape changes (circle, ellipse, parabola, or hyperbola) with different angles. The core mathematical concepts include conic sections in solid geometry, the intersection of a plane and a curved surface, and spatial rotation and projection. The construction uses GeoGebra commands such as Line to define the cutting axis, Rotate to rotate the plane, and IntersectPath to compute the intersection curve between the plane and the cone surface, with objects eq1, f, n, p, and c for parameter control. It is suitable for upper secondary or early university students to understand the geometric nature of conic sections, and also serves as a classroom demonstration tool for teachers to build intuitive 3D understanding of quadratic curve classification.