Geometric Visualization of a Sheaf of Planes

This example visualizes how a “sheaf of planes” can be organized in geometric space by displaying an interacting family of planes and the resulting consistent intersection structure. The key mathematical ideas include: planes (Plane), determinant-based linear dependence/feasibility checks (Determinant), and the computation of intersection paths or shared intersection geometry (IntersectPath). Construction-wise, it uses Plane to create multiple plane objects from given points and auxiliary elements, applies Determinant to encode the algebraic condition tying plane positions/parameters together, and then leverages IntersectPath to render the intersection path(s) or overlap behavior among the constructed objects. The included points/objects (e.g., A, B, C, D, E, and parameters such as a, b, c, M, d, f) work together in the same coordinate system to make the inter-plane relationship visually concrete. Suitable for high school honors through early university learners, especially for lessons connecting linear algebra with coordinate/solid geometry and for geometry-focused modeling exercises.