Pythagoras tree

The Pythagoras Tree is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher Albert E. Bosman in 1942, it is named after Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to depict the Pythagorean theorem .

The construction of the Pythagoras tree begins with a square. Upon this square are constructed two squares, each scaled down by a linear factor of ½√2, such that the corners of the squares coincide pairwise. The same procedure is then applied recursively to the two smaller squares, ad infinitum.

Links

• Gallery of Pythagoras trees
• Pythagoras tree with different geometries as well as in 3D
• Three-dimensional Pythagoras tree
• MatLab script to generate Pythagoras Tree