Dynamic Slanted Cone: Interactive 3D Geometry Exploration

This example demonstrates a dynamically adjustable slanted cone in 3D space, where dragging control points or sliders updates the cone's tilt angle, base position, and generator lines in real time, visually contrasting slanted and right cones. Core mathematical concepts include solid geometry definitions of cones, generators, base circles, vertex projection, cross-sections (ellipses, circles), and perpendicular relationships between lines and planes. Construction uses GeoGebra commands: Line for generators, OrthogonalLine for perpendiculars, Point for key vertices, Tangent for base circle tangents, Intersect for intersection points, and Segment for edges; objects include vertex A, base center B, generator f, auxiliary lines a/b/c, and intersection points E/F, all linked parametrically. Suitable for high school and above for studying solid geometry and spatial reasoning, also useful in university analytic geometry or math modeling to explore cross-section properties (e.g., elliptical sections) and intuitive verification of volume formulas.