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.

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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

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