Playground Swing: 3D Geometric Modeling and Motion Simulation

① This example constructs a playground swing in the GeoGebra 3D Calculator, demonstrating the three-dimensional geometry of the swing frame, seat, and its swinging motion. ② Core mathematical concepts include 3D coordinate geometry, points and segments, parametric equations of circles, surface generation (e.g., the seat), rotational transformations, and the Pythagorean theorem for calculating support heights, along with quadratic functions and optimization problems (e.g., relationship between swing angle and height). ③ Construction highlights: the Circle command creates the top ring or reference circle for the swing path, Surface generates the seat or frame surfaces, Point and Segment define key vertices and connecting rods; objects R, A, r, c, n, a, B, f represent radii, points, parameters, etc., with sliders controlling the swing angle for dynamic rotation. ④ Suitable for upper secondary to early university students, this serves as a practical tool for teaching solid geometry, introductory 3D modeling, geometric transformations, and function applications, as well as a visual aid for physics topics like simple pendulum motion.