MORE ON PAPERFOLDING

It is a common knowledge that folding a sheet of paper yields a straight line. We start our discussion of paperfolding with a mathematical explanation of this phenomenon. The model for a paper sheet is a piece of the plane; folding is an isometry of the part of the plane on one side of the fold to another, the fold being the curve of fixed points of this isometry (see Figure 1). The statement is that this curve is straight, that is, has zero curvature.