Parametric Torus Surface Modeling in 3D

This example demonstrates how to construct a torus (a doughnut-shaped solid) as a smooth 3D surface in GeoGebra, illustrating how a complex geometry can be generated continuously from parameters. The main mathematical ideas are parametric surfaces, trigonometric parameterization, and 3D analytic geometry/coordinate modeling. The construction is carried out using the GeoGebra command Surface to render the surface. From the provided construction summary, objects b, a, c act as geometric parameters controlling the torus shape, while tx, ty, tz represent the computed x/y/z coordinate components. The parameters tt and tu correspond to the variables used to sweep the surface (typically angle-like parameters), linking trigonometric expressions to spatial coordinates. Suitable for late secondary school through early university students, and useful for lessons on parametric equations, trigonometry, and solid geometry visualization.