Constructing Non-Self-Intersecting Polygons from Point Lists

This GeoGebra example demonstrates how to take an unordered list of plane points, sort them according to a geometric rule, and connect them in sequence to form a simple polygon with no self-intersections. The construction illustrates core concepts in computational and Euclidean geometry, including polygon simplicity, self-intersection avoidance, point-set ordering, and closed polygonal chains. Built with GeoGebra commands Sort, Sequence, and Polygon, the example uses objects A through Z along with auxiliary objects such as original, Z, original_h, original_s, and the resulting poly1. It is suitable for high school geometry, undergraduate analytic geometry, and GeoGebra dynamic construction tutorials, offering a concrete model for teaching simple polygon construction and basic computational geometry algorithms.