# Variations on Pythagoras' Tree

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When constructing a Pythagoras' tree, you start with a right-angled triangle and three squares. For a detailed explanation see Pythagoras & Thales. Then you build a tree recursively. By using Thales' theorem, you can vary the triangle by moving the vertex at the right angle along a circle. This is how you make an animated Pythagoras' tree.

## The tree types

The first (leftmost) tree type is a regular animated Pythagoras' tree.

The second tree type is made by drawing an open curve between four vertices of each square. The **tightness**
of the curve varies.

The third tree type is made by drawing **one** open curve along the left and right branch of the tree.
The vertices at the right angle of each right-angled triangle are shown as dots.

The fourth tree type is made by drawing **one** open curve along the left and right branch of the tree.
Then one such branch is drawn for each sub-tree.

## Animated gifs

Pink Pythagoras tree on tumblr.

## The code

The processing-code can be seen at OpenProcessing: Variations on Pythagoras' Tree.