THE
FIBONACCI RATIO
A E B F
D C G
Figure
1-5 Golden section of a rectangle.
Greek architects and sculptors incorporated this ratio
into their work. Phidias, a famous Greek sculptor, made use of it; the
proportions of the Parthenon at Athens illustrate this. Built in the fifth
century B.C., it is based on a triangular pediment, which is still intact. Its
dimensions exactly fit into the Golden Rectangle. It stands as an example of
the aesthetic value of this unique shape.
The
Logarithmic Spiral
The only mathematical curve to follow the pattern of growth is the
logarithmic spiral, expressed in the spiral mirabilis or the nautilus shell
(Figure 1-6). The logarithmic spiral is called the most beautiful of
mathematical curves. This spiral has been a common occurrence in the natural
world for millions of years. The Golden Section and the Fibonacci series are all
associated with this remarkable curve.
Figure 1-6 shows
a radiograph of the shell of the chambered nautilus (nautilus pompilius). The
successive chambers of the nautilus are built on the framework of a logarithmic
spiral. As the shell grows, the size of the chambers increases, but their shape
remains unaltered.
We will
demonstrate the geometry of the logarithmic spiral using the Golden Rectangle
ABCD (Figure 1-7) with AB :BC = phi: 1. Through point E,
called the "Golden Cut" of AB, line EF is drawn perpendicular to
AB cutting the square AEFD from the rectangle. The remaining
rectangle EBCF is a Golden Rectangle. If the square EBGH is lopped
off, the remaining figure HGCF is also a Golden Rectangle. Assume that
this process is repeated indefinitely until the limiting rectangle 0 is so small
that it is indistinguishable from a point. Forex 101.
Forex Art Of Fibonacci (Forex 101)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15. 16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
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27.
28.
29.
30. 31.
32. 33.
34.
35.
36.
37.
38.
39.
40.
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44. 45.
46.
47.
48.
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51.
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63. 64.
65.
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71.
72. 73.
74.
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78.
79,
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85.
86.
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88.
89. 90.
91.
92.
93.
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95.
96.
97.
98.
99.
Forex Art Of Fibonacci (Forex 102)
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114. 115.
116.
117.
118. 119.
120.
121. 122.
123.
124.
125. 126.
127. 128.
129. 130.
131.
132.
133.
134. 135.
136.
137.
138.
139.
140.
141.
142. 143.
144.
145. 146.
147.
148.
149.
150.
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152.
153. 154.
155. 156.
157.
158.
159.
160.
161.
162.
163.
164.
165. 166.
167.
168.
169.
170.
