Fibonacci Number and Ratio Analysis
10.9.2 the geometrically based approach to
Fibonacci Operations
We now see what happens when we use a geometrically based approach on a loga-
rithmically scaled chart. Refer to Figure 10.36. Notice that the three geometrically
derived retracement levels are now associated with different values. The previous
38.2 percent retracement level price of $465 is now $295. The other two retrace-
ment percentages of 50 percent and 61.8 percent also display a change from $390
to $234 and $316 to $190, respectively. Due to the compression effects at higher
prices inherent on logarithmically scaled charts, the percentage retracement values
will tend to decline to lower values when measured geometrically.
We also see in Figure10.36 that geometrical symmetry is not preserved on logarith-
mic charts. For example, we expect to find the physical distance from the 50 percent
level to either the 38.2 percent or 61.8 percent to be of equal distances. But we observe
that this is not the case. We find that, in our chart, there is a price difference of $61 be-
tween the 38.2 percent and 50 percent retracement levels, whereas the price difference
between the 50 percent and the 61.8 percent levels is only $44. This does not occur
on arithmetically scaled charts, as numerical and geometrical symmetry are preserved.
Therefore in summary, when employing arithmetically scaled charts, retrace-
ment levels may be determined by using either the numerical or geometrical
approach. There will be no price discrepancy in the values of the respective re-
tracement levels and geometric symmetry will be preserved. Conversely, when em-
ploying geometrically scaled charts, retracement levels should only be determined
via the numerical approach. This will ensure that the retracement values are con-
sistent with those on arithmetically scaled charts.
Note that since geometrical symmetry is not preserved on logarithmically
scaled charts, the use of proportional dividers (a popular Fibonacci percentage
measuring tool) will yield inconsistent results. Proportional dividers should there-
fore only be used on arithmetically scaled charts.Figure 10.36 Geometrically Based Retracements on a Logarithmically Scaled Chart.
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