# Another cubit approximation

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:

₢ == 10²/φ²π²ⅇ²

or

(10/φπⅇ)² cubit approximation

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:

MethodValueDifference from π/6Abs difference
π/60.523598775598300.000000000000000.00000000000000
φ²/50.523606797749980.000008022151680.00000802215168
Ave Year0.523607797087850.000009021489560.00000902148956
π – φ²0.52355866483991-0.000040110758390.00004011075839
10²/π²φ²ⅇ²0.523764440990030.000165665391720.00016566539172

If we really want to keep root 2 happy, we could rewrite it like this, and cheat a bit.

Cubit with tau, phi, e and root 2

Where tau τ is equal to 2 π.