Spinning Cube and the Belt Trick (Belt Trick) Visualization

This example demonstrates the “Belt Trick” phenomenon by animating a spinning cube in 3D: even after an apparent nontrivial twist, a carefully chosen continuous motion can return the object to its initial orientation without abrupt discontinuities. Key ideas include rigid-body rotations in space, transformation-driven motion, and parameterized curves/paths used to visualize how the rotation evolves over time. Construction relies on GeoGebra commands CurveCartesian and Rotate: CurveCartesian is used to create Cartesian curves that serve as motion-related trajectories/auxiliary loci, while Rotate applies a continuous rotation by an angle α to the cube. Intermediate objects such as speed and setup parameters, together with computed vector/point components (e.g., CrossX/CrossY/CrossZ, KX/KY/KZ, and coordinate differences like PMinusKX/PMinusKY/PMinusKZ), organize the rotation axis and update positions. Dot helps mark key points corresponding to important configurations. The result is a clear interactive geometric demonstration for understanding continuous spatial transformations. Suitable for upper secondary school through introductory university courses on solid geometry, transformation geometry, and math visualization.