Constructing Golden Rectangles: Geometric Construction and Ratio Exploration

① This example demonstrates how to construct a golden rectangle, a rectangle whose side lengths are in the golden ratio (approximately 1.618), and explores its inherent spiral and proportional relationships. ② Core mathematical concepts include the golden section, golden ratio, similar rectangles, the geometric manifestation of the Fibonacci sequence, and the recursive property of subdividing the rectangle into squares. ③ Construction highlights: Based on the construction summary, the example uses GeoGebra objects such as Rectangle, Line Segment, Function Graph, Surface, and Linear Functions, likely to draw segments, define ratio relationships, or use sliders to dynamically adjust dimensions, possibly incorporating random experiments to show ratio stability. ④ Suitable for high school to early college mathematics classes, this resource is ideal for teaching geometric construction, ratio concepts, or interdisciplinary explorations between mathematics and art, providing a dynamic visual aid for understanding the appearance of the golden ratio in shapes.