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Frank Reed you wrote: "I saw a comment today taking note of today's date as a 3:4:5 triangle in the Pythagorean Theorem. Written in mm/dd/yy format (popular US style), today is 9/16/25. See it??"

I'm afraid I don't see 9/16/25 as a '3:4:5' triangle.  81+256 does not equal 625.  However, 9/12/15 would be a '3:4:5' triangle.  Nevertheless, I see what the writer was getting at.

As to the second part, some checking is required first to see if a paper 3:4:5 triangle applied to a globe with one short side aligned along a meridian ends up with the other short side aligned with a parallel of latitude for all positions on the globe, as the same would be true for declination and SHA.  Then some calculations will be required although there are some similarities with ‘Difference Between Rhumb Line and Great Circle Distances’ tables as per Table V of AP1618 1941 edition except these are rather coarse.  DaveP