Transformation of Pyramid: From Solid Geometry to Complex Spheres

①This example demonstrates a dynamic transformation of a pyramid (tetrahedron-like four-sided pyramid) in 3D space, where vertices, edges, and faces change position under parameter adjustments, linking to spheres, complex numbers, and centroids. ②Core mathematical concepts include solid geometry of pyramids, representation of complex numbers in space, sphere equations, centroid/barycenter, and exponential transformations affecting the geometric shape. ③Construction highlights: using GeoGebra commands Point, Polygon, Pyramid, Circle, Center, Segment, Angle to build the base pyramid with objects A, B, C, D, poly1, a, b, c, d, E, e, faceABE, faceBCE, faceCDE, faceADE, edgeAE, edgeBE, edgeCE, edgeDE, then f, F, G, poly2, g, a_1, b_1, h, i, α for transformations. ④Suitable for high school to university teaching of solid geometry, complex numbers, and spatial transformations, also useful for dynamic geometry exploration and mathematical modeling, helping students intuitively grasp connections between 3D shapes and algebraic expressions.