Diameter.
Radius.
Circumference.
Chord.
Arc.
6. The law of mediation of contrasts is shown as follows: the semicircles, when placed on the table with ends towards right or left, connect points of opposite direction up and down, and when placed with ends pointing upward or downward they connect the right with the left side.
The circle is of course an unending line traced from a given point back to itself, according to certain laws, but it is also a union of two semicircles curving outward in opposite directions. "It is a representation of the general law, since the periphery and centre stand in contrast to each other, and are connected by the radii."—(Froebel.)
The New Gift and its Charms.
Having already analyzed straight lines in the sticks, we will pass directly to the consideration of the ninth in the series of Froebel's gifts, the rings, which are whole, half, and quarter circles of bright silvered wire.
If the sticks were fascinating to the child as the embodied straight edge or line, and perfect treasure-houses of new possibilities to the kindergartner, the rings are just a bit more delightful as, with their glittering surface and curved lines, and their wonderful property of having neither beginning nor end, they are quite different in appearance from anything which precedes or follows them. Of course the child sees at once that here is an entirely new field for invention, and he hastens to possess it, fully conscious of his power of combining the new elements.
Introduction of the Ring.
We must first discuss the new form with the children so as to be certain that they fully understand its relation to the other gifts. Perhaps in a previous exercise with the eighth gift we have allowed the children to experiment with a stick, and to break it partially in a number of places so as to produce a measurably correct curved line, afterwards promising them that they should soon have perfect curves to play with. This exercise has its value because it illustrates practically that a curved line is one which changes its direction at every point.
Let us see when to-day's play begins if the children can think of any way to make such curves, save by the stick already used. Some quick-witted little one will remember at once the surface of the ball and his repeated experiments in dividing it, and will suggest in sufficiently plain words that a curved line might be made from a clay sphere. His neighbor thinks a clay cylinder would make one more easily, and both experiments are tried by all the children with a resultant of quite perfect clay rings. Then some one wants to make paper rings, and some one else cloth rings, and the wise kindergartner encourages all this experimenting, knowing that "the power of memory increases in the same ratio as delight, animation, and joy are connected with free mental activity."