Parametric Construction and Geometric Analysis of a Torus

This example demonstrates the generation and geometric properties of a torus in 3D space. The core mathematical concepts involve parametric equations, surfaces of revolution, and differential geometry. The construction utilizes the 'Surface' command to create the main body, 'CurveCartesian' for cross-sectional circles, and the 'Derivative' command to analyze surface slopes and tangents. Key objects include parameters for the major radius R, minor radius r, and the rotation angle $\phi$, along with segments and angles to define the geometry. This model is ideal for high school solid geometry, university multivariable calculus, or computer graphics students to visualize parametric surface logic.