Exploring Cross-Sections of 3D Solids

This applet demonstrates the construction and exploration of cross-sections in 3D solid geometry, focusing on figures such as tetrahedra and pyramids. By explicitly defining the vertices, edges, and faces of a 3D solid, the applet uses intersection commands to generate the cross-sectional polygon formed when a plane cuts through the solid. Users can dynamically adjust the position, orientation, and tilt of the cutting plane using interactive sliders or draggable controls, observing in real time how the shape, size, and number of sides of the cross-section change as the plane moves through different positions within the solid. The opacity of the cutting plane and the solid itself can also be adjusted, allowing students to see both the interior cross-section and the outer structure of the solid simultaneously. This visual transparency supports a deeper understanding of how a plane intersects edges and faces at various heights, making it easier to identify patterns such as triangular, quadrilateral, or pentagonal cross-sections depending on the cutting angle and location. The applet reinforces key geometry concepts including planar sections, spatial reasoning, and the relationship between a solid's structure and the shapes produced by intersecting planes. It serves as an effective interactive learning tool for students studying立体几何 (solid geometry), helping them move from static textbook diagrams to dynamic, exploratory visualization. By manipulating the cutting plane and immediately seeing the resulting cross-sectional polygon, learners can test conjectures, discover geometric properties, and build intuition about how 3D objects are sliced in space, making abstract spatial relationships concrete and accessible.