Square Construction with Similarity Transformation and Circles

① This example demonstrates how to construct a square using intersections of circles, lines, and polygons, and then apply a similarity transformation (scaling) to generate related figures, showing dynamic geometric relationships. ② Core mathematical concepts include properties of squares, circle geometry, similarity transformations (homothety or scaling), and intersection relationships among points, lines, and circles. ③ Construction highlights: Based on the construction summary, GeoGebra commands such as Intersect, Point, Circle, Line, and Polygon are used, involving objects like points A, B, C, D, E, F, G, lines c, d, f, g, circle e, polygon poly1, and auxiliary objects a, b, f_1, g_1. The square vertices are determined via intersections, and a similarity transformation generates scaled copies. ④ Suitable for upper middle school or high school students to understand geometric construction, similarity transformations, and circle applications, and for teachers to demonstrate dynamic geometry.