Pythagorean Tree

This print was created for Math 401: Mathematics though 3D printing of Fall 2019, at George Mason University taught by Professor Evelyn Sander.

The Pythagorean Tree is an Iteration function that iterates vertically upwards. Between each of the Squares lies a 45 degree right triangle where the bottom square represents the length of the Hypotenuse and the two squares above it represent the lengths of the sides. There is 4 iterations displayed.

To produce the first iteration, start with the original square and then scale by cos(45) and translate up by the length of the original square. For the square of the left and rotate counterclockwise by 45 degrees and for the square on the right rotate clockwise by 45 degrees. Repeat this process for each new square to Produce the next iteration.

This function is considered a "tree" because of the image produced by this iteration. The original Square is the trunk and the iterations are the branches and leaves.