If you take a page of flat notebook and try to stand it up by laying it on its edge on a table it’s nigh impossible. But why does it support itself if you simply add a fold along the middle of the page?
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For a far more interesting experiment, try to use a single sheet of paper to bridge a gap between two tables. A flat sheet will fall through, but add a few folds to make a jigzag and it will be much stronger.
The reason is that a flat sheet cannot take on compound curvature. If you deliberately curve (or fold) it in one direction then it cannot curve also in the other direction. To do so would require it to stretch which it strongly resists.
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