Cone Surface: Dynamic Construction from Points, Segments to 3D Surface

This GeoGebra example demonstrates how to construct a cone surface in 3D view, showing its generatrix, base circle, and apex. The core mathematical concepts include the geometric definition of a cone (generated by rotating a right triangle about one leg), the quadratic surface equation (e.g., z² = x² + y²), and properties of equilateral triangles in axial cross-sections. Construction highlights: use Point to create apex A and base center V, Segment to build generatrix l and radius r, Cone command to directly generate the solid, and Locus to trace a moving point D forming the generatrix path. Other objects include B, C, h (height), g (base circle), a, c, b (auxiliary segments/curves), and E, F, f, i as supporting elements. Suitable for high school solid geometry teaching to visualize cone generation, generatrix loci, and surface equations, as well as for university analytic geometry demonstrations of quadratic surfaces.