Colorful Pythagorean Tree: A Fractal Polygon Construction Based on the Pythagore

This example demonstrates a colorful fractal structure known as the Pythagorean tree, built iteratively using squares and right triangles that obey the Pythagorean theorem. The core mathematical concepts include the Pythagorean theorem, properties of equilateral and right triangles, polygon construction, and geometric transformations. Although original tags mention probability and derivatives, the actual content is rooted in elementary Euclidean geometry. The construction employs GeoGebra commands such as Polygon to create base polygons (e.g., poly1), Flatten to manage nested lists, and defines points A1 through A6 along with angle parameter α to control branching orientation and scale. Suitable for middle to high school students learning geometric proofs, fractal visualization, or dynamic geometry software techniques.