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A Golden Rectangle
can be used to construct a Golden Spiral. Any Golden Rectangle,
as in Figure 3-5, can be divided into a square and a smaller
Golden Rectangle, as shown in Figure 3-6. This process then
theoretically can be continued to infinity. The resulting
squares we have drawn, which appear to be whirling inward, are
marked A, B, C, D, E, F and G.
Figure 3-6
Figure 3-7
The dotted lines, which are
themselves in golden proportion to each other, diagonally bisect
the rectangles and pinpoint the theoretical center of the
whirling squares. From near this central point, we can draw the
spiral as shown in Figure 3-7 by connecting the points of
intersection for each whirling square, in order of increasing
size. As the squares whirl inward and outward, their connecting
points trace out a Golden Spiral. The same process, but using a
sequence of whirling triangles, also can be used to construct a
Golden Spiral.
At any point in the evolution of
the Golden Spiral, the ratio of the length of the arc to its
diameter is 1.618. The diameter and radius, in turn, are related
by 1.618 to the diameter and radius 90° away, as illustrated in
Figure 3-8.
Figure 3-8
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