Conic Sections, Rectangles, and 3D Solids: A Comprehensive Exploration (OAF.SAE.

This example demonstrates an interactive construction combining conic sections, rectangles, and 3D solid geometry, with additional elements of interest calculation and trigonometry. The core mathematical concepts include the geometric properties of conic sections, representation of rectangles in plane and space, cross-sections and projections of solids, and the use of trigonometric functions in angle calculations. Construction highlights: using GeoGebra commands such as Point, Vector, Textfield, and Intersect to create points, vectors, text boxes, and intersection points; objects include a_1, f, A_1, B_1, u, text1, text2, inputBox1, x_0, q_x, G1, H1, A1, B1, I1, J1, button1, x_1, text5, g, J, v, K, D, and text3, which build a dynamic model with adjustable parameters via buttons and input fields. Suitable for high school and above, this example is ideal for exploring the connections between conic sections and solid geometry, as well as for mathematical modeling and dynamic visualization.