Pythagoras' Tree

The tree contains all primitive Pythagorean triplets. The root is the triplet (3, 4, 5). Denote the values of a typical node by (s, c, n). The three children of each node are obtained as follows:

Left child:
Let delta = 2*(n + s - c) (s_left, c_left, n_left) = (-s - delta, c + delta, n + delta)
Middle child:
Let delta = 2*(n - s + c) (s_middle, c_middle, n_middle) = (s + delta, -c + delta, n + delta)
Right child:
Let delta = 2*(n + s + c) (s_right, c_right, n_right) = (s - delta, c - delta, n + delta)

Navigate the Tree

To place a node in the root, hold the 'Shift' key down and click on the node
To see the values in the node, click on the node and hold
To move the tree one level up, click on the 'Move up' button

For further details download the article

The Modular Tree of Pythagoras

which will be published in the MAA Monthly.

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