Visualizing the folding-over within the remembered frame of the original square results in an image of the original square divided into square quarters, its quadrants, and the sides of the inner square seem to be diagonals of the quadrants. Many people conclude that the corner triangles can be arranged to cover the inner square exactly, without any gap or overlap. Thence they infer that the area of the original square is twice the size of the inner square. Let us assume that the propositions concerned are about Euclidean figures. Our concern is with the visual route to the following: