Material for Inscribed and Concentric Figures: In this material, which for the most part is made up of that already described, and which is therefore merely an application of it, inscribed or concentric figures may be placed in the white background of the different inset frames. For example, on the white background of the large equilateral triangle the small red equilateral triangle, which is a fourth of it, may be placed in such a way that each vertex is tangent to the middle of each side of the larger triangle.
There are also two squares, one of 7 centimeters on a side and the other 3.5. They have their respective frames with white backgrounds. The 7 centimeters square may be placed on the background of the 10 centimeters square in such a way that each corner touches the middle of each side of the frame. In like manner the 5 centimeters square, which is a fourth of the large square, may be put in the 7 centimeters square; the 3.5 centimeters square in the 5 centimeters square; and finally the tiny square, which is 1/16 part of the large square, in the 3.5 centimeters square.
There is also a circle which is tangent to the edges of the large equilateral triangle. This circle may be placed on the background of the 10 centimeters circle, and in that case a white circular strip remains all the way round (concentric circles). Within this circle the smaller equilateral triangle (1/4 of the large triangle) is perfectly inscribed. Then there is a small circle which is tangent to the smallest equilateral triangle.
Besides these circles which are used with the triangles there are two others tangent to the squares: one to the 7 centimeters square and the other to the 3.5 centimeters square. The large circle, 10 centimeters in diameter, fits exactly into the 10 centimeters square; and the other circles are concentric to it.
These corresponding relations make the figures easily adaptable to our artistic composition of decorative design (see following chapter).
Finally, together with the other material, there are two stars which are also used for decorative design. The two stars, or "flowers," are based on the 3.5 centimeters square. In one the circle rests on the side as a semi-circle (simple flower); and in the other the same circle goes around the vertex and beyond the semi-circle until it meets the reciprocal of four circles (flower and foliage).
III
SOLID GEOMETRY