Pythagoras Tree Tool

This example demonstrates the dynamic construction of the classic Pythagoras tree fractal, where squares are recursively built on the sides of right triangles, producing a tree-like branching pattern. Core mathematical concepts include the Pythagorean theorem, similar triangles, symmetry, exponential growth, and curve sketching. Construction highlights: the GeoGebra command PythagoraTree automatically generates the tree structure, while Polygon is used to create base squares; objects include n (iteration count), vertices A through V, triangles t1–t4, squares q1–q8, and recursively generated points Z, A_1, B_1, C_1, illustrating recursion and iteration. Suitable for middle/high school math classes or geometry exploration, this tool helps visualize the geometric meaning of the Pythagorean theorem, fractal self-similarity, and exponential complexity, and serves as an engaging introduction to mathematical art and algorithmic thinking.