Animation 4: Parabola, Pythagorean Theorem, and Fractal Geometry

① This example demonstrates a dynamic animation that visually connects a parabola, the Pythagorean theorem, fractal geometry, median lines, arithmetic mean, and variance, offering a multi-concept mathematical exploration. ② Core concepts include parabola, Pythagorean theorem, fractal geometry, median line, arithmetic mean, and variance, bridging algebra, geometry, and statistics. ③ Construction highlights: Based on the summary, GeoGebra commands such as Line, Parabola, Point, OrthogonalLine, Intersect, Dilate, Segment, Angle, and Rotate are used, with objects A, B, a, C, c, D, b, E, d, C', e, D', f, α, β, C'_1, C'', e', and a button (button1) to drive the animation through rotations, dilations, and intersections. ④ Suitable for high school and above, this is ideal for teachers and students to explore geometric transformations, fractal generation, and statistical visualization in an interactive lab setting.