THE FIBONACCI RATIO IN GEOMETRY
Both the
spiral and ellipse have unusual properties consistent with the Fibonacci ratio
in two dimensions, price and time. It is very likely that the integration of
spirals and ellipses will elevate the interｭpretation and use of the Fibonacci
ratio to another, much higher level. Up to now the Fibonacci ratio was used
for measurement of correcｭtions and extensions of price swings. The time
element forecast was seldom integrated because it did not seem to be as
reliable as the price analysis. By including spirals and ellipses in a
geometric analysis, both price and time analysis can be combined accurately.
The Golden Section of a Line
The Greek mathematician Euclid related the Golden Section to a straight line
(Figure 1-4). The lineAB of length L is divided into two segments by point C.
Let the length of AC and CB be a and 6, respecｭtively. If C is a
point such that L :a equals a \b, then C is the Golden Section AB.
The ratio L :a or a :b is called the "Golden ratio." In other
words, the point C divides the line AB into two parts in such a
way that the ratios of those parts is 1.618 and .618.
|-覧覧覧覧L 覧覧覧与|
Golden cut Figure 1-4 Golden section
of a line.
The Golden Section of a Rectangle
In the Great Pyramid, the rectangular floor of the King's chamber ilｭlustrates
the Golden Section (Figure 1-5). A "Golden Rectangle" can best be demonstrated
by starting with a square葉he basic area of the Pyramid of Gizeh. Side AB
of the square ABCD in Figure 1-5 is bi-sected. With the center E
and radius EC, an arc of a circle is drawn cutting the extension ofAB
at F. Line FG is drawn perpendicular to AF, meeting the
extension of DC at G. Then AFGD is the Golden Rectangle.
According to the definition, the Golden Section Rectangle is 1.618 times
longer than it is wide. The ratio of its proportions is therefore phi:
1.618:1 Forex 101.
