Geodesics on a Cone: Construction and Visualization

This GeoGebra example demonstrates how geodesics are traced on a conical surface, highlighting the way shortest-path curves behave on a curved solid. It focuses on the geometric meaning of geodesics, the correspondence between the cone and an appropriate planar representation (via unfolding-style geometry), and the parameterized construction needed to generate smooth curves on the surface. The core build uses GeoGebra commands Plane, Surface, and CurveCartesian: Plane defines the reference spatial setting, Surface creates the cone geometry, and CurveCartesian uses a parameter (e.g., t) together with computed parameters such as R, l, w, and height/radial relations to generate the geodesic curve on the 3D surface. Points and helper objects (e.g., A, B, C, and labeled text objects) are used for key geometric references and annotations. Suitable for secondary-to-university geometry/solid-geometry instruction, and for early exploration of differential-geometry ideas through dynamic visualization.