The Addition Law: Geometric Demonstration on the Unit Circle

① This example demonstrates the geometric meaning of vector addition using points on the unit circle and polygons, showing how two vectors combine head-to-tail to form a resultant vector. ② Core mathematical concepts include vector addition, the unit circle, the parallelogram (or triangle) law, and relationships between angles and coordinates. ③ Construction highlights: GeoGebra commands such as Random generate random points, Textfield and InputBox allow user input, Polygon constructs polygons (e.g., poly1, poly2), Intersect finds intersection points, and a button (button1) triggers dynamic updates to explore different addition scenarios. ④ Suitable for high school or early college students learning vector operations and geometric intuition, as well as for teachers demonstrating the visual representation of the addition law in class.