While poking around Giza, I stumbled on this approximation for the inverse of the fine structure constant. It’s not as good as my previous one, but since it relies on cubit -> metre conversion, it qualifies as “interesting.”
It’s just 100φ² ₢, expressed as metres, So we just multiply that by π/6, and voila!
Which according to Wolfram Alpha,
100 / (100φ²π/6) / (fine structure constant)
is 99.9679457% accurate …
Well, according to the current known value, which is a moving target.