Ellipse Construction on a Sphere

This example demonstrates how to construct an ellipse on a sphere, illustrating a generalization of the ellipse definition in spherical geometry. Core mathematical concepts include spherical geometry, the ellipse definition (sum of distances to two foci is constant), spatial relationships among points, lines, and planes, and locus generation. Construction highlights: using GeoGebra commands such as Intersect, Sphere, PointIn, Line, Circle, Point, Plane, IntersectPath, Midpoint, Segment, OrthogonalPlane, and Locus, the example builds foci and a moving point on the sphere, then generates the ellipse as a locus based on distance constraints. Suitable for high school or university courses in solid geometry, analytic geometry, or mathematical modeling, this helps students intuitively grasp the connection between spherical geometry and classical conic sections.