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.
Extensive reading is considered as an effective way to improve English skills, not only of reading but also of listening
and even of speaking. Many junior high schools, senior high schools, colleges, Kosens, and cram schools across the
country include extensive reading in English in their curriculum today. Preparing reading materials, however, costs a lot of money and takes a wide space, and also managing extensive reading class is quite difficult. This paper reports how we built an extensive reading library and how the author has used these materials in classroom and also in open classes in the past six years.