The references below aver that the following is not crudely trivial:
The shortest curve between two points is a (straight) line.
An elementary school teacher construed it as follows (which I now register as the contrapositive):
If you don't walk to the other point in a straight line, then you must be walking more distance to get there.
Is there an improved intuition of this result? I am not asking for any proof or formal argument. Please forgive me should this be a duplicate.
I referenced ♦ The shortest distance between any two distinct points is the line segment joining them.How can I see why this is true?,
♦ http://www.thestudentroom.co.uk/showthread.php?t=52233,
♦ P117-119 of A Guided Tour of Mathematical Methods for the Physical Sciences by Roel Snieder.