Angle-driven geometric construction for solids and functions

This GeoGebra exercise demonstrates how geometric relationships—especially angle constraints—can be used to build and connect a solid/section-like configuration in a dynamic way. It highlights the interplay between key points and segments, angle measurement/control, and function-based relationships (e.g., polynomial/function objects) to support reasoning about the resulting figure. Core concepts include solid-geometry construction ideas, angle definition and interactive angle motion, and using functions to encode or relate geometric behavior. Construction-wise, it uses Line and Segment to form the structural skeleton, Angle to define the critical angles, AngleMoverCW to make the configuration respond to clockwise angle changes, and Point to specify and control key locations; the objects/parameters A, B, C, D, f, g, α, i, i_2, and β organize the geometry and the underlying parameters/relations. Suitable for high-school to early university students studying geometry-construction, dynamic geometry, and geometry–function connections.