Folding a sheet in half, nothing could be simpler! Constructing the midpoint of a line segment via origami is thus nothing too tricky, and it already proves simpler than in classical straightedge-and-compass geometry. Starting from a square sheet with side 1, we can therefore obtain a length of 1/2. Can other lengths be obtained? Folding a sheet into three already seems a bit trickier. Through successive trials, you may get the impression of managing reasonably well, but an exact construction would be more satisfying.
No need to bend over backwards! ----------------------------------
Take a square sheet and mark the midpoint of the top side. Now bring the bottom right corner to the midpoint of the top side and admire the result.
To make studying the resulting figure easier, we can introduce some notation, as shown in the drawing below.