ONION: Parametric Surface Visualization of an “Onion-Like” Shape

This example demonstrates how to build and visualize a continuous parametric surface whose geometry resembles an “onion-like” layered 3D form. The key mathematical ideas include parametric surface representation, mapping parameters to 3D coordinates, and using angular parameters (with trigonometric functions) to generate a structured spatial shape; the construction is typically linked to quadratic or radial/ellipsoidal-style geometry. From the construction summary, the figure is created with GeoGebra’s Surface command to form the surface object s, using parameter objects ρ, θ, ϕ and shape/control parameters a, b. Here, ρ acts as a radial/layer parameter, while θ and ϕ serve as angular parameters that drive how points are placed in space; a and b control the shape scale or deformation. Suitable for high school advanced geometry, early university calculus/analytic geometry topics on parametric curves and surfaces, and for classroom or self-study visualization of parameter-driven 3D models.