[brgross]

I went with great circles since that feels like the most “natural” straight line on a sphere — the path you’d walk if you just kept going forward without steering. You could define "straight" as a constant compass direction (I think it's called a "rhumb") -- that would look straight on a Mercator map but would actually require regular steering adjustments to maintain the bearing.

[munchler]

That makes sense, but I think constant latitude, in particular, is a special case that people often have in mind.

[zamadatix]

The other methods are about defining different meanings of what "going around" actually is while constant latitude is a special case of many such methods, e.g. great circle, not a new definition of what going that way means.

[munchler]

I'm not sure what you mean, but a circle of constant latitude is definitely not a great circle (except on the equator).

[zamadatix]

You're 100% right, I conflated great circle and small circle there.