For example, Britain’s national mapping organisation’s brand is associated in our national consciousness with going to a small shop in a quaint village to get a map showing how to walk up a mountain. It’s called Ordnance Survey. If that sounds like Artillery Research to you, that’s because the project started because the king wanted to know how to accurately bomb Scotland.
of course the shortest distance is a straight line, that’s literally the definition of a straight line.
The point is that you can’t follow a straight line on a globe, because that’s longer than taking a slight curve. If you take a straight line, you follow the entire circumference of the earth, but following a curved path allows you to avoid some of the width. Basically, the circumference means a straight line is more curved than a curved path.
i don’t even understand what you think ‘straight’ and ‘curved’ even mean at this point.
I’m talking about how in this image, the upper curved line is shorter than the straight line that follows the equator:
Because the curvature of the earth is greater than the curvature of the upper line. So by taking the upper curved line, you “skip” some of the curvature of the earth.
that line only appears straight because of the map projection being used. the one that appears curved is actually straight on a globe. you could construct a different projection that made that straight line appear straight (though other straight lines would thereby be distorted instead). latitude lines are not straight lines, and never have been, except the equator.
Isn’t it still a straight line from the perspective of someone travelling it? It just appears curved because you’re looking at it from outside the curved surface.