In the use of the circle in design one of the simplest forms suggested by Book V is the trefoil (three-leaf), as here shown, with the necessary construction lines. This is a very common ornament in architecture, both with rounded ends and with the ends slightly pointed.
The trefoil is closely connected with hexagonal designs, since the regular hexagon is formed from the inscribed equilateral triangle by doubling the number of sides. The following are designs that are easily made:
It is not very profitable, because it is manifestly unreal, to measure the parts of such figures, but it offers plenty of practice in numerical work.
In the illustrations of the Gothic windows given in [Chapter XV] only the square and circle were generally involved. Teachers who feel it necessary or advisable to go outside the regular work of geometry for the purpose of increasing the pupil's interest or of training his hand in the drawing of figures will find plenty of designs given in any pictures of Gothic cathedrals. For example, this picture of the noble window in the choir of Lincoln Cathedral shows the use of the square, hexagon, and pentagon. In the porch of the same cathedral, shown in the next illustration, the architect has made use of the triangle, square, and pentagon in planning his ornamental stonework. It is possible to add to the work in pure geometry some work in the mensuration of the curvilinear figures shown in these designs. This form of mensuration is not of much value, however, since it places before the pupil a problem that he sees at once is fictitious, and that has no human interest.
