Great Circle on a Sphere: Intersection of a Plane and a Sphere

① This example demonstrates the construction of a great circle on a sphere, which is the intersection of the sphere with a plane passing through its center and two points on the sphere. ② Core mathematical concepts include spheres, great circles, plane-sphere intersections, spatial geometry of points, lines, and planes, and circle properties. ③ Construction details: using GeoGebra commands such as Sphere to create the sphere, PointIn to place points on the sphere, Plane to define a plane through the center and two points, IntersectPath to obtain the intersection curve, and Point, Center, Segment to mark key points, the center, and radius segments, resulting in a complete great circle visualization. ④ Suitable for high school or college solid geometry courses, this example helps students intuitively understand spherical geometry, great-circle routes (e.g., shortest paths on Earth), and the intersection of planes and curved surfaces in 3D space. It serves as an effective teaching tool for three-dimensional geometric concepts.