One of my hobbies is sacred geometry - loosely defined, it’s the study and use of mathematical archetypes in nature and culture, often with a focus on traditional compass and straightedge constructions.

Don’t worry; I’m not about to go off into numerology, telling you that you can derive the groovy cosmic secrets of the ancients by studying numeric coincidences. I actually take a rather dim reading spurious meaning into special cases of the Interesting Number Theorem.* The worst case scenario might resemble the Arronofsky film “Pi”, except without the sweet soundtrack.

Nonetheless, exploring the traditions behind sacred geometry can give insight into art and design. The traditional compass and straightedge drove the development of mathematics until just a century or two ago, and modern algebra has its roots in questions about why it is, exactly, that you can’t construct a perfect heptagon. The practice is also fun and relaxing, and can even give occasional insights into physical reality.

One subject that comes up a lot in these discussions is a number called the golden ratio, sometimes abbreviated phi. Phi is defined in terms of the relationship between a line segment and its parts. Continue reading