Distances and Grades

Interesting discussion at Ask MetaFilter: the original question wasn’t phrased this way (or all that well), but essentially it’s whether changes in elevation make any difference in the distance travelled. For example, is a road with a lot of 10 percent grades up and down longer than a perfectly flat road? Basic trigonometry suggests that it is, but in practice, it’s not much more than a rounding error. And besides, the distances indicated on road maps — a point in the original question — would have taken that into account.