# GEOMETRY OF FORMS

The forms presented here are (1) triangle (three sides), (2) square (four sides), (3) pentagon (five sides), (4) hexagon (six sides), and (5) octagon (eight sides). Figures 10-8 through 10-12 illustrate how each of these polygons is formed within a circle, respectively. Figure 10-8
Developing an equilat­eral triangle within a circle. Most people can estimate the location of the center of a circle rather easily with a pencil or pen. Figure 10-15
The form of the circle and square fit within each other. These four directions create blind spots at the square’s corners. This type of activity can stimulate design cre­ativity and make designing an exciting process. of the circle. Lines that don’t point to the circle’s center are apt to seem awkward or unrelated in their relationship with the circle (left side of Figure 10-5). The Circle
Among the many and varied forms we see in the world around us, the circle stands out as being unique. Most design themes, including those described in this book, are strongly related to two fundamental geometric shapes: the circle and the square. This reinforces the axial nature of the square. In other words, lines and edges that form a 90-degree relationship to a circle’s circumference are more stable looking than compositions that lack this relationship. the circle’s a’pcubfference
Figure 10-6
Lines should meet the circle’s circumference at 90 degrees. Radii are lines that originate at the center of the circle and extend outward to the cir­cumference. As has been shown, the circle and square along with their component parts are the foundation for a limitless variety of design compositions. Square

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Figure 10-10
Developing a pentagon within a circle. First, the center is a point that inherently attracts attention. Those com­positions in which lines meet the circle’s circumference by utilizing an extended ra­dius are apt to be more pleasing than those that don’t (Figure 10-6). In a similar fashion, the manner in which lines and forms meet the circle’s cir­cumference helps determine whether or not a composition is successful. Another idea for developing compositions with a square is to use it as a modular grid. Equilateral polygons can be used in developing design compositions and can be formed within a circle. Unlike a circle, the square does not face outward in all direc­tions (Figure 10-14). Figure 10-13
The square is inherently divided by two axes, which are parallel to its sides and pass through the center. Fferrtagan

Figure 10-11
Developing a hexagon within a circle. Because design involves the development of alternative ideas, it is important to realize that numerous design compositions can be generated by exploring the relation­ships possible among the basic components of a specific form. Two noticeable axes in a square pass through its center and are parallel to the sides (Figure 10-13). The Square
A square, unlike a circle, is often considered a human-made form because it is made up of straight lines and is not found in nature. As one engages in this type of activity, new forms are discovered that give rise to new ideas. (Figure 10-18). Extended radii are similar, but extend beyond the circle’s circumference. All four sides are equal in length, and the interior angles each measure 90 degrees. Figure 10-14
Unlike the circle, the square does not face outward in all directions. Hexagon

Figure 10-12
Developing an octagon within a circle. A square’s configuration suggests an axis (a centerline) that divides the form into equal halves. relationships with Strong relationships with
the circle’s orcumference. Diagonals can be added to the previous grids to provide different de­sign compositions (Figure 10-19). Because of its simplicity and completeness, the circle has often been described as the most pure or perfect form. For example, these smaller squares can be one-half, one-quarter, or one-third the length of the original square’s sides. The center is, of course, the middle point

Figure 10-4
Component parts of the circle. The square is also a formal form, owing to its symmetrical structure. The circumference, or outer edge of the circle, defines the limits or edge of the circle. So, one of the first considerations for designing with a circle is to realize that any line that directly points to a circle’s center will create a strong relationship with the circle (right side of Figure 10-5). Figure 10-7
Various design compositions are possible when focusing on the component parts of a circle. The circle has a number of components that are critical to its use in a design composition.

Updated: 31.10.2014 — 05:59