Dynamic Exploration of Dini’s Surface: A Constant Negative Curvature Surface

This example uses interactive visualization to explore Dini’s Surface and highlight how a constant negative curvature surface behaves visually as its parameters change. The core ideas include parametric surfaces, geometric intuition from differential geometry (negative curvature), and the construction of surface coordinates using trigonometric functions. The geometry is built in GeoGebra with the Surface command, using the objects listed in the construction summary—a, b, c, d, e, testo1, testo2, and testo3—to parameterize and control the resulting surface and its auxiliary elements. The original theme also points to the use of rotation and trigonometry (cosine and sine) in the underlying parametrization. Suitable for upper-secondary through early university learners, especially for calculus/geometric modeling lessons and investigations of parametric curves/surfaces.