Turning Polygons: Dynamic Geometric Art with Tangent and Scatter Plots

① This example demonstrates how rotating polygons can generate dynamic mathematical art, combining geometric transformations with function graphs to create visually rhythmic patterns. ② Core mathematical concepts include polygons, line segments, rotation (transformation), difference and slope, tangent function, and scatter plots, highlighting the interplay between algebra and geometry. ③ Construction details: Using GeoGebra commands such as Sequence, Polygon, Textfield, and Length, the construction builds multiple polygon lists (trilist, quadlist, polylist) and point sequences (list1, list2, etc.), with sliders/input boxes (InputBox1-3) controlling parameters (a, b, c, d) and rotation steps (n, skip), and text objects (text1, text2) displaying dynamic values, ultimately producing rotated polygon sequences and scatter plots. ④ Suitable for upper secondary to early university students, this is ideal for exploring geometric transformations, functional relationships, and mathematical art creation, as well as for math experiments or interdisciplinary projects.