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I constructed this geometric shape trying to replicate an illustration I found in Miranda Lundy’s book Sacred Geometry. (And admittedly I also had to look up some instructions from Andrew Sutton’s Ruler & Compass: Practical Geometric Constructions.)

The caption in Lundy's book suggests that we can find the size of the moon relative to the size of the earth by using a pentagon, as shown. (In the drawing there are two circles which are outlined with a solid black line: those circles represent the moon and earth.)

So is this geometry sacred, as the title of Lundy’s book suggest? I guess that depends on your definition of sacred. And perhaps on your view of the world. Leaving the gods out of it for now, I asked somebody smarter than me to check the idea mathematically — it was something with tangent, I believe? — and I was told the data and the math pretty accurately supports the illustration!

And had it not been accurate, the drawing would still be worth the effort. The pursuit of beauty is a goal in itself.

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