Recently I read the answer to a question proposed by someone on this site.

The question : What is the rate of curvature per mile on Earth?

The answer given : Use Pythagoras' Theorem to solve for the answer, given a 1 mile side

and a side as the radius. The hypotenuse minus the radius is your answer of drop/mile or curve/mile.

My conjecture : Why go through all of that work if the distance is one? Something like

{1/diameter} would would fine for such a problem. Seems like a lot of work for no reason.

I understand the practical application of Pythagoras' Theorem in this certain situation, as you would need

to use a^2+b^2=c^2 for any distance greater than one [mile]..

It just seems excessive and unnecessary if you're solving for curve / one mile.