Fathauer Right Triangles and a Mathematical Art Spiral

This example demonstrates how a sequence of “Fathauer right triangles” can be built via repeated geometric transformations to form a spiral-like mathematical artwork, showing a self-similar/fractal-style visual effect. Key concepts include right-triangle construction, similarity through scaling (dilate) and rotation (rotate), and iterative sequence-driven geometry generation (sequence). In GeoGebra, the construction uses Line and OrthogonalLine to define supporting lines and perpendicular constraints; Point and Intersect to locate vertices from intersection relationships; Polygon to draw each triangle; Dilate and Rotate to transform triangles step by step; and Sequence to generate an ordered family of objects that trace the evolving spiral geometry (e.g., parameters and successive points such as those represented by r2, l1, and rotated/scaled variants). The result highlights how iterated transformations create a structured spiral from simple right-triangle rules, making it suitable for high school to early university learning, classroom activities on geometric construction, and math-art explorations.