Dynamic Exploration of Dini's Surface

This example demonstrates the famous Dini's Surface, a helical surface with constant negative Gaussian curvature discovered by Italian mathematician Ulisse Dini. The core mathematical concepts include parametric surface equations, constant negative curvature, helical surface construction methods, and the differential geometric properties of surfaces. Construction details: Using GeoGebra's Surface command with parametric equations x=a·cos(u)·sin(v), y=a·sin(u)·sin(v), z=a·(cos(v)+ln(tan(v/2))+c·u), where parameter a controls the overall scale of the surface and parameter c determines the degree of helical twist, while sliders b, d, and e are used to dynamically adjust the surface morphology. Suitable for differential geometry, parametric surface studies, and visualization teaching in university mathematics courses, also serving as an introductory example for mathematics majors to understand negative curvature surfaces.