Parabolic Cylinder: Dynamic Construction and Visualization

This GeoGebra example demonstrates the 3D shape of a parabolic cylinder and its dynamic intersections with planes and curves. The core mathematical concepts include cylinder equations, quadric surfaces, space curves, projections, and generating surfaces via transformations. Construction highlights: from the summary, the IntersectPath command is used to compute intersection curves, involving objects such as k, i, c, a, cuad (quadrilateral), rotasi/rotano (rotations), ejessi/ejesno (axes), buttons (botón3, botón1), point e, p, curve c1, and surface cu. This indicates that rotations, translations, and button interactions control the viewpoint and parameters, dynamically showing how the parabolic cylinder intersects with cutting planes. Suitable for high school solid geometry, university analytic geometry, or multivariable calculus surface visualization, and useful for interactive mathematical exploration and teaching.