Pool Shot #1: Geometric Path Construction

This GeoGebra example demonstrates the geometric construction of a pool shot path in 3D space, using spheres, segments, and circular arcs to model the cue ball's direction and rebound trajectory. The core mathematical concepts involve 3D vectors, spherical geometry, arc construction, and piecewise functions to describe the path segments. The construction employs GeoGebra commands such as Segment, Point, CircumcircleArc, and Circle, with numerous labeled objects (A through Z) and auxiliary lines (a through m) to define key points on the sphere and arcs that determine the shot direction. The piecewise function captures the path's turns. Suitable for high school or college geometry lessons, as well as physics demonstrations of collision and reflection, helping students visualize spatial reasoning and vector applications in a realistic context.