The accurate division of a circle into two equal comma-shaped areas of the special shape presented by the "Tomoye" of the Japanese (Fig. 54) and the rotating "Great Monad" of Chinese cosmogony (Fig. 55), is effected by describing within a given circle two circles each having its diameter equal to a radius of the enclosing circle. The two inscribed circles touch one another at the centre of the latter, but do not overlap. The area of the enclosing circle is thus divided into four areas, _a_, _b_, _c_ and _d_ (see Fig. 60, A). The areas _a_, _b_ are the two inscribed circles. Each of the residual areas _c_, _d_ is called (as Sir Thos. Heath, F.R.S., kindly informs me) an "arbelus" by ancient Greek geometricians–a name used for a rounded knife used by shoemakers. The comma-shaped bent cone or pine is formed by the fusion of one of the two small circles with one of the adjacent arbeli (Fig. 60, B). The figure so formed which to-day is loosely spoken of as a "bent cone," a "pine," or a "comma," has never, so far as I can ascertain, received a name in geometry, nor in the language of decorative design or pattern-making. Nor has the S-like line made by the two semicircles separating the contiguous "pines" or "commas" received any designation though vaguely indicated by the word "ogee." The comma-like areas might conveniently be called "streptocones," and their S-like boundary "a hemicyclic sigmoid." As shown in Fig. 56, by drawing a second hemicyclic sigmoid of the same dimensions at right angles to the first, the circle is divided into four smaller streptocones. By using sigmoids or half-sigmoids of a curvature of a different order from that of the hemicyclic one, but of a precisely defined nature, the circle may be divided into three, six, eight or more equal "streptocones" of graceful proportions, some of which have been used either in series as borders in metal work (for circular dishes and goblets) or as detached or grouped elements in pattern-designs (stone-work tracery, embroidery, woven and printed fabrics).