3D Surface Plotter via Rotation (Hyperbola-Related Shape)

This example demonstrates how to build and visualize a 3D surface in GeoGebra, using rotation/transform ideas to obtain a hyperbola-related spatial shape. It connects the geometry of a surface (surface plot) with the rotation process that turns curve structure into a volumetric-looking form. Key concepts include surfaces, hyperbola-related geometry, rotation (Rotation) as a construction method, and calculus connections such as derivatives (Derivative) and geometric quantities like the centroid or barycenter (Centroid or Barycenter) when analyzing the surface’s overall characteristics. The construction workflow is mainly: define the generating curve/relationship, apply rotation/transform operations to generate the surface, then optionally compute and display derivative-related information and centroid/barycenter measures. It is suitable for high school advanced geometry, early university analytic geometry, and calculus visualization lessons where students benefit from seeing geometric and differential ideas in 3D.