Intersecting Three Cylinders and Their Cross-Section Curves

This example visualizes the “penetration”/overlap of three cylinders in 3D space and renders the resulting intersection (cross-section) curves, allowing students to inspect how complex spatial outlines emerge from intersecting surfaces. The key math concepts are solid geometry with cylindrical surfaces, curve-of-intersection (crossing curves) between 3D surfaces, and the use of rigid transformations—especially rotations and reflections—to build the symmetric or oriented configuration of the solids. Construction-wise, it leverages GeoGebra commands Surface and CurveCartesian to create the cylinder surfaces (zyl1, zyl2, zyl3) and to plot the intersection curves (k1–k4, l1–l2, m1–m2). Rotate and Mirror are used to reposition or generate additional cylinder-related parts so that the three-cylinder setup yields meaningful intersection curves. Text1 provides annotations for clarity. Suitable for secondary to undergraduate audiences learning spatial geometry, transformation-based construction, and the visualization of surface intersections.