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!

137.0799391

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.