リンゴの皮むき曲線について

抄録

Using a spherical model of an apple-peel fold-out, we derive a formula that, for a given cut width, describes the corresponding S-shaped spiral with Archimedes spirals on both ends. From numerical calculation of the formula when the cut width becomes finer, we obtain that, rescaling a sequence of spirals by making them a unit length, the shape of these spirals tends to a well-defined limits, called lituus. From intrinsic equation of an apple peel curve, we show that the curve consists of Euler spiral from around the equator of the sphere and Archimedes spirals around the ends.