As previously shown (here and here), φe/8.4 is a good approximation (0.5236) for the Royal Cubit.

But, you may ask, what’s so special about 8.4?

Well the 8.4 is actually the simplified version of the numbers that came out when deriving the relationship. But we can go in the other direction as well, and explode 8.4 into various components and equivalent fractions.

8.4 formulas

We can do some exposition as follows:

Click image to enlarge.

8.4 exposition