A couple weeks ago, all us students were given a workshop lecture on sacred geometryby Cynthia Lapp. Sacred Geometry is essentially the use of simple geometric relationships to create incredible shapes, generally associated with religious structures. For a long time (and still today depending on who you ask) geometry has been associated with higher reality due to its physical manifestations of mathematics, the most ideal and conceptual of sciences. Circles, for example, are both infinite and one, since their shape is defined by a single unit extended in every possible direction. Triangles have long been associated with the three-fold nature of God in Christianity, and are also a throwback to Greek philosophy. In several different world religions, God is considered the “Great Geometer.”
I was immediately taken with it, though not entirely for the same high-minded reasons that enraptured humanity’s greats. I’ve always loved math, even more so when I discovered algebra. Algebra is really just about relationships between numbers, which can then be represented beautifully through geometry.
I find pure constructed geometry beautiful, more so when it is done by hand. There is something of the carpenter’s craft in it. Imagine the drafter of only a couple decades gone, hunched over his desk late into the night, the only sounds made with the scratch of graphite and compasses and architecture rules.
Until the information age, it had been this way in some form or another for literal millennia. As Cynthia explained, most craftspeople’s wealth was in the patterns they could create. While anyone could purchase pattern books that would reveal how to construct hundreds of different patterns, the most complex and beautiful ones were often not recorded. Others were sealed for royal or religious use only, and some were even banned from use.
Until iterative computing could perform millions of iterations quickly to determine how exactly to recreate these patterns, some of them had been lost for hundreds of years, with men and women trying to understand how to recreate them with just a couple compasses and straightedge. Even if they were successfully pondered out, the sheer precision of these etchings can be near-impossible to retrieve.
I was immediately drawn to it. The image below was the product of that workshop. It took twenty minutes to create, and it was one of the simpler designs.
I’ve taken to carrying a compass on me at all times. I’ve gotten into the habit of seeking out sacred geometry whenever I enter a mosque. If I find a pattern I think I can puzzle apart, out comes the compass and straightedge.
This is one of my favorite things about the process. I am a very visual thinker, and with my love for math it is simultaneously fascinating and rewarding to break down the relationships between shapes, to try and figure out a way to create a certain fractional unit of a shape. And every time, it starts with a simple circle. Incredible.
A recent experience that will go down in the mental record books happened a few days ago. It was the evening after studio, and we were all tired from class. We climbed the stairs together into our studio space. For most of us it was to pick up our stuff and head home, for others a time to work on a project. I decided to work.
Somehow, it came up that my classmate (and roommate) Peter had been trying to produce a pentagon using only a compass and a straightedge (no ruler), and had so far been unsuccessful. I was intrigued by the idea. Peter, Skyler and I inscribed, wrote little formulas, drew diagrams, and puzzled with the hopes of producing a perfectly shaped pentagon using the archaic but timeless tools. By the time I was done, I had burned two hours and a dozen pages in my sketchbook.
Pentagons are hard. Triangles, squares and hexagons are your simple building blocks. Surprisingly, hexagons are the easiest; they are made by using the same unit as the radius of the circle, so no change or calculation need be applied to compass measurements. Triangles are slightly harder, but only because they require actual effort. Squares require a little discovery and thinking the first time that you try. But pentagons? Pentagons are hard.
My first attempts were absolutely unsuccessful. Mostly I putzed around, looking for relationships between points and trying them out on the unit circle. No luck. Thankfully, my brain pulled out a fact from a book I read years ago that somewhere within a pentagon is the golden ratio. Recalling how to make this ratio became the first step.
With time, intuition and a little serendipity, I resolved the golden rectangle and produced this little absurdity. For those curious, the golden ratio is the diving board into the world of fractals and self-similar geometry, used by humanity’s greatest, as well as nature. Constantly.
With the golden ratio in tow, I began to diagram with rough stars. I played out the shapes, compared them to my ratios, and eventually concluded on the likeliest relationships.
This is where things get strange. I produce this piece of work, but it doesn’t satisfy me. Why not? Well, in the process of working it out, I produced a pentagon first, and then inscribed the circle of its five points. I wanted to do the exact opposite.
After another hour of reverse engineering my pentagram and the pentagon that Skyler produced from an instructional video, I finally resolved it. Bask in its geometric glory.
The discovery was flood of dopamine. I felt incredibly accomplished to produce the shape.
It’s still mind-blowing to me to think that such elegance can be created from such simple tools, truly the tools of the ancestry of architecture. Even on a program such as Adobe Illustrator, the process is the same, if simplified for the sake of efficiency and accuracy.
After thousands of years, geometry still rules our world. Some things don’t change.