Geometric Visualization of a Stick Shadow: Angles, Locus, and Limits

This example models the classic “shadow of a stick on the ground” scenario to visualize how the shadow position changes with a geometric parameter such as the sun elevation/angle. It highlights the asymptotic behavior suggested by the limit idea when the angle approaches extreme values. The construction centers on geometric intersection and parameterized angle relationships: using Intersect to find intersection points, Line/Circle/CircumcircleArc to create the guiding lines and arcs, Point/Segment/Center to define key locations and circle centers, and Angle to control and measure the driving angle (e.g., θ, α/β). A Locus object generates the moving shadow endpoint’s trajectory as the parameter varies, while Vector supports directional/scale relations. Suitable for secondary-to-early-undergraduate students learning geometric construction, trigonometric/angle modeling, and using GeoGebra for intuitive limit-based exploration.