Pythagoras Fractal Tree Macro: Recursive Right-Triangle Construction

This GeoGebra macro demonstrates how a Pythagoras-based fractal tree is generated by repeatedly constructing and attaching right-triangle shapes using consistent side-length and angle rules. The key math concepts are the Pythagorean-triangle relationship as the guiding idea for scaling, trigonometry for determining connection angles, and geometric transformations that reuse local reference points to grow the figure step by step. Construction-wise, it creates polygonal (triangle) components with Polygon and tracks their defining vertices using Point/Vertex; it uses Centroid to obtain reference locations for each stage; it measures lengths via Length to control scaling; it computes angles with Angle to set the correct orientation; and it applies Translate to move newly created parts into position for the recursive “tree” growth. The example is driven by a control like button1 and uses stored objects such as A, B, C, D and auxiliary points/values (e.g., VC, VD, CR/CL, dL/dR, side, angR/angL, sR/sL, poly1) to manage geometry and parameters. Suitable for middle/high school through early university lessons on geometry construction, recursion, and fractal visualization.