From Cylinder to Sphere: A Geometric Transformation Demo

① This example demonstrates the continuous transformation of a cylinder into a sphere using dynamic geometry, making the relationship between 3D solids visually intuitive. ② Core mathematical concepts include solid geometry (cylinder and sphere), geometric transformations such as mirroring and rotation, volume calculation, and the use of sequences and sums for constructing intermediate shapes. ③ Construction highlights: The GeoGebra commands used are Vector, Sequence, Sphere, Mirror, Volume, Sum, Line, Circle, and Cylinder, with objects including R, k, E_1, E_2, u, v, l1, a, l2, l5, l3, b, l3', l5', c, d, e, f, text1, text2, l6, g, h, p, i, q, and j. These elements are combined to create a parameter-driven morphing effect. ④ This is suitable for high school or early college students studying solid geometry and transformations, and is also valuable for math lab activities or inquiry-based learning to enhance spatial reasoning and conceptual understanding.