The Pythagoras Headdress

The Pythagoras Tree is based on some pretty simple mathematics. Basically, you start with a square, and then add two more on top of it in a triangle configuration. If you use a right triangle with 45 degree corners, this is easy to do on graph paper, since each daughter square is √2/2 the size of the parent square, then the corners of each square will always line up with the graph paper until the graph squares are bigger than the tree squares.



This is the blank slate. I numbered the rows and columns, then figured the shape of the first square out. Since the final tree will be about 6 x 4 times the original shape, I was able to make the first square 2" x 2". Luckily Staples had huge graph paper. What would I do without Staples (in this one particular instance).



After a couple of generations, I was unable to use the ruler at all. However I still think that using cardboard taped to a free IKEA ruler is a damn cool way to measure stuff.



By the time I was done drawing boxes, I had drawn 511 boxes of varying sizes. There's nine generations there.



Here Kristin started her work, which was definitely harder. We ended up filling in the spaces in between boxes as well as the boxes themselves, which created a better final look but took a long time.



Hard at work again. It's hard to see the detail in these pictures but each different size square in each generation has its own pattern, and when the boxes overlap their colors change in very interesting ways.



Some of the larger boxes were painted, due to their size and also for the aesthetic benefits.



That's me, Steve, on the left, and Kristin on the right. Kristin did most of the detail work and I did the dumb stuff, like shading hundreds of spaces brown.



This is the finished product, at least as far as painting and markering goes.



After cutting out the tree, we used this cardboard to hold the shape.



This here is the finished product... one Pythagoras Headdress.