Function Art 3D: Building a Pawn with Intersecting Surfaces

This GeoGebra example demonstrates how to create a 3D “pawn-like” sculpture by defining several function surfaces and then computing their intersection curves/lines to shape the silhouette and internal segmentation. It highlights core ideas such as function-based surface modeling (algebraic and trigonometric-style expressions), surface intersection (Intersect) to carve boundaries, and curve sketching for controlling where parts meet. Construction is driven by the listed commands Surface and Intersect: surfaces corresponding to objects f, g, j, p, q are generated, and intersections with additional controlling quantities (α, d, A, B, a, b, e, l, c) determine the final composite geometry. Several text objects (text1–text5) are used to annotate steps or key parameters. Suitable for high school to early university students studying functions, graphing, and solid geometry, as well as learners interested in mathematical visualization and function art projects.