Rotating a Spiral: Dynamic 3D Surface

This GeoGebra example dynamically demonstrates a spiral curve rotating around an axis to generate a three-dimensional surface, vividly illustrating how a planar parametric curve transforms into a spatial solid. The core mathematical concepts involve parametric equations, trigonometric functions, rotational transformations, and differential equations (as spirals often relate to Archimedean or logarithmic spirals). The construction uses the CurveCartesian command to define the 2D spiral, the Surface command to create the rotational surface, and sliders a, n, b to control the radius, number of turns, and rotation angle, enabling interactive exploration. Suitable for high school to undergraduate students studying parametric curves, spatial surfaces, and transformations, as well as for mathematical modeling or artistic spiral design.