After fiddling around a bit, eventually found another way of getting an approximation for the royal cubit. I say approximation because, compared to the other methods, it’s only accurate to about 3 decimal places.
The formula looks like this:
What I like about it is how it uses what are arguably the most famous numbers of all time in all of mathematics (yes, √2, you’ve just been demoted) and wraps them all nicely to produce a reasonable figure for the royal cubit.
Not quite as elegant as Euler’s famous formula, but still interesting.
By way of comparison, here’s the others:
|Method||Value||Difference from π/6||Abs difference|
|π – φ²||0.52355866483991||-0.00004011075839||0.00004011075839|
If we really want to keep root 2 happy, we could rewrite it like this, and cheat a bit.
Where tau τ is equal to 2 π.