Golden Ratio Root Convergence Visualization

This GeoGebra example demonstrates the iterative convergence to the golden ratio (φ) as a root of a quadratic equation through geometric construction. It integrates algebra, geometry, and sequences, showing how successive approximations approach the fixed point. Core concepts include the golden ratio, quadratic equations, limits of sequences, similar triangles, and dilation transformations. The construction uses commands such as Intersect, Point, Segment, Line, OrthogonalLine, Polygon, and Distance, with objects labeled A through N, lines f–n, and text boxes text1–text4. Sliders or parameters n_1 and m_1 control the iteration steps, while distance d tracks the error. Suitable for high school or early college students to explore the connection between algebraic roots and geometric convergence, and to visualize the self-similar nature of the golden ratio.