Projective Construction on a Sphere: Lines, Complex Numbers, and Quadratics

This example demonstrates a projective geometric construction on a sphere, involving intersections of lines, planes, and the sphere to reveal relationships among straight lines, complex numbers, and quadratic curves. Core mathematical concepts include spherical geometry, projective geometry, complex number representation, quadratic equations, and quadrilateral properties. The construction uses GeoGebra commands such as Sphere, Segment, OrthogonalPlane, IntersectPath, Rotate, Intersect, Plane, and Point, with objects including sphere center O, point A, line a, point Z, plane f, path p, circle c, and derived points A', A'_1, A'_2, etc. Suitable for high school to undergraduate geometry courses, this example helps visualize projective transformations and the role of complex numbers in geometric configurations.