Pythagoras and Plato, but not Patrick

I think I have a sort of strange hybrid of OCD and ADD. I get really, really, obssesive about some arcane subject, but only for a very short period of time, and then I’m swiftly on, obsessively studying some other strange topic.

This is part of why I’m a 31 year old undergrad. I keep changing my major.

Some of my wierd interests have started to congeal into a strange project. I have written previously about Scalable Vector Graphics. I have been having an on-again, off-again interest in them. I have roughly similar interests in pre-socratic philosophy, and in pre-Christian Celtic mythology.

So, I started out with a simple enough idea: I would draw an equilateral triangle in SVG. This got to the essense of why vector graphics are so cool. You draw a triangle, the same way you define one, simply by defining the location of the three vertices.

This got me thinking about Plato. With SVG, you don’t make an equilateral triangle, you make the equilateral triangle. You define the form of the triangle.

This was all very well and good pseudo-bullshittery, but I had to figure out how to tie down my triangle onto a cartesian coordinate system. This turned out to be a bit more complicated that I thought, because the Pythagorean Theorem doesn’t apply to equilateral triangles. I had to beat my head against Google for a while before I remembered that the Pythagorean Theorem could be generalized as the Law of Cosines.

After I figured that part out, it was not a big deal to pin down my verticies.


My three verticies
The three verticies with some extra junk.

The reason for the extra dot in the center is that I was reading a tutorial on how to draw Celtic Knots, and somehow figured out that the world-famous triskelle was actually based on the equilateral triangle. Some people know the triskelle as the “trinity knot”. This is a blasphemy. People were drawing these things long before the dark times. Anyways, I digress.

So, I modified my objective. I would now make a triskelle out of SVG.

I tried a few paper sketches, then I make a crude SVG version.

The framework of the Triskelle

Trigonometry is fun.

Now, I had a perfectly minimalist triskelle. It was around this point that I, after staring into the code for about 4 hours, decided that there was great wisdom in Pythagorean Mysticism. Numbers really were the fundamental building blocks of reality.

When you find yourself gaining metaphyical insight from a piece of XML, it is probably a good time to step away from the computer. However, I kept right on going.

My knot was perfect, but it lacked substance. So, I thickened the lines and gave it some color.
I also had to draw the crosshatching which give the illusion that certain parts of the knot are actually underneath other parts.

A triskelle cartoon

Too computer-perfect

This is where I expected to be done with the project, but I didn’t like the way it looked. It looked too perfect, too computer-generated, and too cartoonish. So, I set out to muck it up a bit. Basically, I created a new layer over it, and traced. Then i went through and removed as many nodes on the paths as possible, to try to create a more organic look.

This is what I ended up with:

A triskelle cartoon

It’s finally starting to look like something.

If you are at all interested in any of this foolishness, you can have a look at the final SVG file. Be aware, it’s not 100% pure SVG, Inkscape puts a bit of extra crap in it.

By the way, all these pictures, the SVG file, and all of the photographs on are licensed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 license.

Creative Commons License

Leave a Reply

Your email address will not be published. Required fields are marked *