Deformations of a Solid: Interactive 3D Geometric Morphing

This GeoGebra example demonstrates the continuous deformation of a three-dimensional solid (such as a sphere) under parametric control, using sliders and buttons to animate the shape from its initial form into complex variations like twisting, expansion, or contraction. The core mathematical concepts involve solid geometry, differential geometry (curvature and deformation), and algebraic parameterization through variables like α, β, n, and others. The construction uses GeoGebra commands Join and Sequence to generate point sets and segments, building the deformation framework. Key objects include parameters a, m, Form, A, β, α, n, RR, Speed, e, h, along with lists liste1 through liste4 storing critical points or loci, and images image1/image2 with buttons Bouton1/Bouton2 to control animation and reset. This resource is suitable for high school to university-level mathematics instruction, particularly in solid geometry, differential geometry, or computer-aided geometry, helping students grasp the mathematical essence of parametric deformation and dynamic geometric transformation.