A variation of the paper strip method 1 uses the observation that the midpoint formula_297 of the paper strip is moving on the circle with center formula_298 (of the ellipse) and radius formula_299. Hence, the paperstrip can be cut at point formula_297 into halves, connected again by a joint at formula_297 and the sliding end formula_302 fixed at the center formula_298 (see diagram). After this operation the movement of the unchanged half of the paperstrip is unchanged. This variation requires only one sliding shoe.