Summary: Given a piece of foldable material (e.g. paper) in the shape of a right-angled triangle. Fold it by placing the right-angled corner on the hypotenuse. How should this be done in order to minimize the area of the folded triangle? The problem leads to a cubic equation whose relevant solution turns out to involve an angle trisection (and thus obtainable by a succession of foldings). Variations of the problem are considered, in particular letting one of the acute corners instead be placed on the opposite side.