Hyperboloid of One Sheet Constructed with String Segments

① This example demonstrates a one-sheet hyperboloid visualized by connecting corresponding points on two parallel circles with straight segments, forming a ruled surface mesh. ② Core mathematical concepts include the ruled nature of hyperboloids, parametric representation of surfaces, and spatial transformations such as translation and rotation. ③ Construction details: using GeoGebra commands Point, Sequence, Intersect, Vector, Translate, Rotate, and Segment, the model generates point lists (list1, list1', list2) and connects them to create the characteristic string-art appearance. ④ Suitable for high school to undergraduate courses in solid geometry, analytic geometry, or computer-aided geometry, as well as for mathematical modeling and artistic visualization of quadric surfaces, helping learners grasp the generation of ruled surfaces and the geometric properties of hyperboloids.