# The Nautical Mile

The nautical mile has a chequered history. The basic idea was to have it set to one degree of arc of the circumference, but that depends on what latitude you are at. You can read Wiki’s take for some background.

Anyway, yes, that royal cubit can be related to a good approximation of the nautical mile, given that the exact definition has varied over time. It’s currently “defined” at 1852 metres.

Depending on whether we use pi/6 or a rounded version of .524 metres, we get slightly different results, on either side of 1852. Of course this trick is done the the favourite assistants pi and phi, and 10².

The nautical mile.

If we replace ₢ by π/6, we can simplify the first equation down to this:

Nautical mile simplified

Who’da thunk, huh?

But wait! there’s more…. using the approximations from Pi, phi and e, we can rewrite that equation as 7 x 720/e, which is 5040/e. Plato had a lot to say about 5040. So we can rewrite that yet again into this masterpiece of eloquence:

Nautical mile in terms of e