Utility Manual for the Precision Ratio Compass - Elliott Wave ...

Elliott Wave Educational Video Series 

Utility Manual 

for the 

Precision Ratio 

Compass 

Workbook 7

The Elliott Wave Educational Video Series — Workbook 7: Utility Manual for the Precision Ratio Compass 

WORKBOOK 

for the 

ELLIOTT WAVE EDUCATIONAL VIDEO SERIES 

WORKBOOK 7 

UTILITY MANUAL for the PRECISION RATIO COMPASS 

Copyright © 1985, 1987 and 1995 

by Robert R. Prechter, Jr. 

Printed in the United States of America 

First Edition: June 1985 

Second Edition: September 1987 

Third Edition: April 1995 

For information, address the publishers: 

Elliott Wave International 

P.O. Box 1618 

Gainesville, Georgia 30503 

ISBN: 0-932750-25-7 


10 Volume videotape set including workbooks 

ISBN: 0-932750-13-3 


Tape 7 and Workbook 7: 

Introduction to the Elliott Wave Principle 

NOTICE 

All charts are copyright © Robert R. Prechter, Jr. 1990 or have been previously 

copyrighted by Elliott Wave International, Robert R. Prechter, Jr., or other 

entities. All rights are reserved. The material in this volume may not be reprinted 

or reproduced in any manner whatsoever without the written permission of the 

copyright holder. Violators will be prosecuted to the fullest extent of the law. 

2


Page 

5 Introduction 

CONTENTS 

7 PART 1: FIBONACCI AND THE COMPASS 

9 What are Fibonacci Ratios? 

13 Why Fibonacci Ratios? 

15 Compass Terminology and Procedure 

16 Compass Scales 

16 What the Compass Does 

17 Chart Scales 

17 Price and Time 

19 PART II: ELLIOTT WAVE APPLICATIONS 

21 Typical Wave Structure 

22 Using the Compass 

25 Fibonacci Ratio Relationships 

26 Contracting Fibonacci Ratios (for “Retracements”) 

31 Expanding Fibonacci Ratios (for “Multiples” and extensions) 

35 A Complete List of Known Reliable Relationships Within Patterns 

35 Impulse Waves 

35 Fifth Waves When Wave Three is Extended 

35 Extensions in First or Fifth Waves 

3


36 Corrective Waves 

36 Zigzag Corrections 

37 B Waves in Zigzags 

38 C Waves in Zigzags 

38 Flat and Irregular Corrections 

39 B Waves in Flats 

40 C Waves in Flats 

40 B Waves in Irregular Corrections 

41 C Waves in Irregular Corrections 

41 Subwaves in Double and Triple Threes 

42 Subwaves in Contracting, Ascending and Descending Triangles 

43 Subwaves in Expanding Triangles 

44 Advanced Ratio Application — A Comprehensive Forecasting Method 

46 Real-Time Examples of Fibonacci Multiples and Retracements 

46 The Bond Market 

49 The Stock Market 

53 The Gold Market 

59 PART III: GANN ANALYSIS 

61 Gann Analysis 

61 The Gann-Blitz Approach 

62 Squaring of Time and Price 

64 1 x 1 lines 



65 Unequal Chart Divisions 

65 Gann Range Subdivisions 

67 Erroneous Use of the Compass 

67 Conclusion 

4


INTRODUCTION 

R.N. Elliott used a time-saving Fibonacci ratio 

calculation device, and his mention of it in “Nature’s 

Law” has prompted many requests for a similar tool. 

Elliott’s design necessitated a two-step recording procedure, 

since he did not have access to a compass specifically 

made for his purposes. Rather than create a copy of 

that more cumbersome tool, we decided to see if we could 

find a compass which would suit our specific needs. A 

long search finally turned up a company that produced a 

Golden Ratio compass, but the construction was cheap 

and the tolerated error much too great. As any trader 

knows, a few cents’ difference on a stock or commodity 

chart can mean the difference between a perfect entry 

and a missed opportunity. 

After much additional searching, we found a 

manufacturer which made compass tools for professional 

draftsmen. We felt that any less quality was unacceptable. 

We’re extremely happy with the tool we’ve found and 

hope you will be, too. 

Your Precision Ratio Compass is constructed of 

chromium plated solid brass, machine tooled to virtual 

precision. The PRC is a slim, handsome professional 

draftsman’s tool, built for a lifetime of use. The spread 

between points can be firmly locked so the compass won’t 

slip when being moved from one position on the chart to 

another. The compass points are sharp and true, so their 

position on the chart can be read with a minimum of 

effort. In sum, the Precision Ratio Compass has been 

thoughtfully designed to give you years of trouble-free 

service. 

The uses of the Precision Ratio Compass are many 

and varied. Fibonacci retracements, Fibonacci price and 

time ratios, as well as all other ratios (from 1:10 to 10:1), 

can all be marked on a chart with a quick movement and 

a minimum of effort. 

5


The following pages will show you in detail how to apply the 

Compass. Undoubtedly there are uses for it which we have yet to 

discover. If you find any, please let us know. Perhaps your ideas will 

appear in the next edition of this manual. 

Robert R. Prechter, Jr. 

Elliott Wave International 

ACKNOWLEDGEMENTS 

This manual would not be here in its present form without the 

effort and talents of David A. Allman. His editing and illustrative 

skills, as well as his dedication to the project, were invaluable in 

attaining the quality we required for the final product. 

Background charts for some of the illustrations were provided 

courtesy of the following sources: 

Trendline (a division of Standard and Poor’s Corp.), 

345 Hudson St., New York, NY 10014 

Daily Graphs (a division of William O’Neil & Co., Inc.), 

P.O. Box 24933, Los Angeles, CA 90024 

Commodity Researach Bureau, 

75 Montgomery Street, Jersey City, NJ 07302 

6


PART I 

FIBONACCI AND THE COMPASS 

7


8


WHAT ARE FIBONACCI RATIOS? 

Fibonacci Ratios are the ratios between numbers 

at a distance infinitely far along in any sequence which 

is derived by adding a number to the previous number to 

obtain the next. Like pi, these ratios are irrational numbers, 

i.e., they cannot be expressed precisely in either 

fractional or decimal form. The “Fibonacci Sequence” is 

the best known and the most basic additive sequence of 

this type. It is derived by adding each number, starting 

with the number 1, to the one just prior to it to obtain the 

next number. Thus, 1 added to nothing gives a second 1. 

1 + 1 gives 2, 2 + 1 gives 3, 3 + 2 gives 5, 5 + 3 gives 8, 

and so on. The first sixteen terms in the sequence are 1, 

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 and 

987. A full mathematical description of the Fibonacci 

sequence can be found in FIBONACCI NUMBERS by 

N. Vorobev, and a description of its relevance to the financial 

markets can be found in Chapters 3 and 4 of 

ELLIOTT WAVE PRINCIPLE (New Classics Library, 

$29). 

Figure 1 

9


Figure 2 

10


As infinity is approached, the ratio between 

adjacent Fibonacci numbers, smaller over larger, is 

.6180339... (phi), commonly abbreviated as .618; the 

inverse (larger over smaller), gives 1.618. 

As infinity is approached, the ratio between 

alternate Fibonacci numbers, smaller over larger, is 

.382; the inverse (larger over samller), gives 2.618. 

The ratios for second alternate Fibonacci 

numbers are .236 and 4.236. 

The ratios for third alternate Fibonacci numbers 

are .146 and 6.854. 

This progression can be continued forever, as 

demonstrated in the bottom row and far right column 

of Figure 2 (from “Historical and Mathematical Background” 

chapter of Elliott Wave Principle). Note that 

each of the decreasing ratios is the result of multiplying 

the preceding ratio by .618 and each of the increasing 

ratios is the result of multiplying the preceding 

ratio by 1.618. It is for this reason that any 

Fibonacci ratio can be calculated with only one or 

two quick and simple steps with the PRC. 

The spiral-like form of market action is repeatedly 

shown to be governed by the Golden Ratio, and, 

as has often been observed, even the Fibonacci numbers 

themselves appear in market statistics more often 

than mere chance would allow. However, it is crucial 

to understand that the numbers themselves have no 

theoretic weight in the grand concept of the Wave Principle. 

It is the ratio which is the key to growth patterns 

of this type because, although it is rarely pointed out 

in the literature, the Fibonacci ratio results from this 

type of additive sequence no matter what two numbers 

start the sequence. Take, for instance, two randomly 

selected numbers and add them to produce a third, continuing 

in that manner to produce additional numbers. 

11


You will find that as this sequence approaches infinity, 

the ratio between adjacent terms in the sequence will 

approach .618... This relationship becomes obvious generally 

before the tenth term is produced (see Figure 3, 

using the starting numbers 17 and 352). Thus, while specific 

numbers making up the Fibonacci sequence are not 

necessarily important in markets, the Fibonacci ratio is a 

basic law of geometric progression, and does govern 

many relationships in data series relating to natural 

phenomena of growth and decay. 

Figure 3 

12


WHY FIBONACCI RATIOS? 

The occurrence of Fibonacci ratios in markets is 

not coincidence, and it is not a mystical numerological 

theory developed in an ivory tower and forced into real 

life situations. When Elliott began to research the markets, 

he had no idea that the Fibonacci sequence would 

be representative of his eventual discovery. What he 

found initially was that the basic Dow Theory idea that 

primary bull markets traveled in three upward phases 

applied to all degrees of market trend, from hourly waves 

to those lasting centuries. From this discovery, he developed 

a system of naming and labeling the different sizes 

of waves, and soon realized that the total number of waves 

in each degree turned out to be a different Fibonacci number. 

In fact, these totals not only produced the Fibonacci 

sequence, but did so exactly, with no omissions and no 

repetitions. 

The discussion below is a reprint from the “Historical 

and Mathematical Background” chapter of Elliott 

Wave Principle, and illustrates this concept. 

We can generate the complete Fibonacci sequence 

by using Elliott’s explanation of the natural progression 

of markets. If we start with the simplest 

expression of the concept of a bear swing, we get 

one straight line decline. A bull swing, in its 

simplest form, is one straight line advance. A 

complete cycle is two lines. In the next degree 

of complexity, the corresponding numbers are 

3, 5 and 8. As illustrated, this sequence can be 

taken to infinity. 

Elliott came to the conclusion, and rightly so, that 

the stock market, as a measure of the value of 

man’s productive capacity, is a direct recording of 

changes in mankind’s progress and regress through 

history. The fact that this process is governed by 

the Fibonacci sequence, furthermore, led to 

13


Figure 4 

Elliott’s ultimate theory that man’s progress 

through history was following a natural law of 

growth often found in nature’s growth/decay and 

expansion/contraction phenomena. 

The Fibonacci ratio enters the picture when we 

realize that the number of waves in a correction approximates 

61.8% of the number of waves in the preceding 

impulse wave of the same degree. The ideal 

irrational number phi (.618...) is approached by 

14


this method the further on breaks down the wave, that 

is, the greater the number of subwaves one counts. Empirical 

evidence reveals, moreover, that Fibonacci ratio 

relationships occur throughout the price structure in markets. 

The following pages will give specific examples of 

the most common occurrences. 

COMPASS TERMINOLOGY AND PROCEDURE 

For the purpose of this manual, we will refer to 

the compass as having points AB (top, narrow end) and 

points CD (bottom, wide end), as shown in Figure 5. The 

procedure for setting the center guide is as follows: Close 

the compass, loosen the center guide nut, set the scale as 

desired, and tighten the nut. The ratio you have chosen 

will remain fixed for whatever distance you now open 

the compass. For the balance of this manual, all distances 

will be designated by a bar underneath the points in question. 

For example, the distance between points A and B 

will be referred to as AB. 

15


COMPASS SCALES 

Generally, proportional dividers are used for dividing 

lines into equal parts, for enlarging or reducing 

length by different ratios, or for dividing the circumference 

of a circle into equal parts. The left hand scale of 

this compass is used for length multiples while the right 

hand scale is used for circle division. 

To relate the two scales, notice that the sequence 

of Fibonacci ratios, 1.618, 2.618, 4.236, 6.854, 11.090, 

17.944, 29.034, 46.978, 76.012..., when multiplied by 

pi, 3.1416..., yields the series 5 + .1, 8 + .2, 13 + .3, 21 + 

.5, 34 + .8, 55 + 1.3, 89 + 2.1 +.1, 144 + 3.4 + .2, 233 + 

5.5 + .3... Notice that the numbers of the first sequence 

on the left-hand (lines) scale of the PRC correspond to 

the numbers of the second sequence on the right-hand 

(circles) scale fo the PRC. One formula illustrating the 

eternal relationship between pi and phi is as follows: 

F n ≈ 100 x π 2 x φ (15-n) , where φ = .618..., n 

represents the numerical position of the term in the 

sequence and F n represents the term itself. The 

number ‘1’ is represented only once. This F 1 ≈ 1, 

F 2 ≈ 2, F 3 ≈ 3, F 4 ≈ 5, etc. 

For example, let n = 7. Then 

F 7 ≈ 100 x 3.1416 2 x .6180339 (15-7) 

≈ 986.97 x .6180339 8 

≈ 986.97 x .02129 ≈ 21.01 ≈ 21 

WHAT THE COMPASS DOES 

Very simply, the distance between points C and 

D will be the multiple of the distance between points 

A and B which is indicated on the left-hand scale of 

the compass. For example, if the compass is set on 

“5”, CD will be 5 times as long as AB. AB, in turn, 

will be 1/5 as long as CD. Because of space 

16


restrictions, the Golden section marking for length has 

been placed on the right-hand scale. 

When the left hand scale of the compass is set at 

Fibonacci multiples, CD will be a Fibonacci multiple of 

AB, while AB will equal the inverse Fibonacci multiple 

of CD. For example, when the center guide reference is 

placed at “GS”, Golden Section (on the right-hand scale 

of the compass), the distance at the narrow end AB will 

always equal .618 of the distance of the wide end CD. 

Conversely, CD = 1.618 x AB. We frequently refer to the 

right-hand scale under “USING THE COMPASS” because 

there is often a convenient equivalent marking 

correspoinding to the Fibonacci ratio we wish to locate 

on the left-hand scale. 

CHART SCALES 

All the charts in this manual use arithmetic scale. 

The difference between arithmetic and semi-logarithmic 

chart scale is that equal vertical distances on arithmetic 

charts reflect an equal number of points traveled whereas 

equal vertical distances on semi-log charts reflect equal 

percentage changes. Empirical research confirms that 

Fibonacci relationships in markets, in almost all cases, 

are based upon the number of actual points traveled, an 

observation which is consistent with the theoretical basis 

for the Wave Principle. To obtain true multiples, the PRC 

must always be used on charts with arithmetic scale. Fortunately, 

this requirement fits the industry standard since 

9 out of 10 chart services use arithmetic scale. 

PRICE AND TIME 

All examples under “USING THE COMPASS” 

refer to Fibonacci price relationships. These relationships 

are always determined by the vertical 

17


Figure 6 

distance covered on a chart by a wave. In these 

examples, do not measure from the actual beginning 

of a wave to the actual end, a process which would 

include time in the calculation, but rather vertically 

to the price level of the end of the wave. 

You will see that in each of the calculations, the 

PRC is placed with one point at the origin of the wave 

to be measured and the other point vertically equivalent 

to the terminus of that same wave. (See Figure 6.) 

Although experience reveals that Fibonacci time 

realtionships are less commonly found in markets than 

Fibonacci price relationships, the PRC can be used to 

discover where in the past or future the Fibonacci time 

multiples lie. Just apply the Compass in exactly the same 

manner as described under “USING THE COMPASS,” 

but do it along the horizontal axis instead of the vertical. 

When reading the instructions, replace the word “vertical” 

with the word “horizontal” and the word “wave” 

with the words “time segment.” 

18


PART II 

ELLIOTT WAVE APPLICATIONS 

19


20


TYPICAL WAVE STRUCTURE 

This graph of one rendition of an ideal Elliott wave 

has been created as a reference for this manual. It contains 

all of the multiples and retracements discussed on 

the following pages. The index numbers starting at 1000 

are for an imaginary market. Actual real-time examples 

begin on page 46. 

Figure 7 

The exercises under “USING THE COMPASS” 

on the following pages involve ratio relationships which 

are commonly found in real-life markets. They will show 

you how to apply the PRC quickly and efficiently to 

project targets based upon many of these measurements. 

Once you’ve mastered the PRC, you should memorize 

the complete list of known reliable wave relationships, 

which begins on page 35. 

21


USING THE COMPASS 

1.00 (equality) 

After closing the PRC, the center guide may be set at any 

point on the scale and either end may be used depending 

upon the length of the wave in question. Place point A 

(or C) at one end and point B (or D) at a vertical equivalent 

to the other end of a recently completed move to 

determine its length. Then, transfer this distance to the 

extreme point of the most recent move to project an 

equivalent length. 

Sample Objective: You wish to mark the level of a 1.00 

multiple of wave (A) as an estimate for the low of wave 

(C). Refer to Figure 8. 

Example: wave (A) = wave (C) 

.50 

Procedure: Close the PRC. Set the center guide at 2 on 

the left hand scale. Place point C at one end and point D 

at a vertical equivalent to the other end of a recently completed 

move. Flip the compass. AB = .50 x CD. 

Sample Objective: You wish to mark a standard 50% 

retracement of the entire advancing wave from ((0)) 0 

through 5 as an estimate for the next correction. A 50% 

correction is likely since it is quite near the typical 

retracement point marked by the previous fourth wave 

low at 4. Refer to Figure 9. 

Example: Next major correction = .50 x entire wave 

22


Figure 8 

Figure 9 

23


As you may have already deduced, all desired ratios 

from 1:10 to 10:1 may be obtained by simply adjusting 

the setting on the left-hand scale (or the right-hand 

scale equivalent) of the PRC. For orientation, if you were 

to set the center guide at 1 on the left-hand scale (lowest 

hash mark), the distance between points A and B, AB, 

and points C and D, CD, would be identical (AB = CD). 

The compass settings for AB/CD relationships most useful 

for market analysis are listed below. 

.50/2.00. Set PRC at 2.00 on the left-hand scale. 

AB = .50 x CD, and CD = 2.00 x AB. 

.618/1.618. Set PRC at GS on the right-hand scale. 


.382/2.618. Set PRC at 8.2 on the right-hand scale. 


.236/4.236. Set PRC at 13.3 on the right-hand scale. 


.146/6.854. Set PRC at 6.854 on the left-hand scale. 


For the most precise application of all Fibonacci 

ratios using the Precision Ratio Compass, however, keep 

the setting on GS. To understand why, take a few minutes 

to study the unique properties of the Fibonacci ratio, 

phi, as presented in the following tables. 

24


FIBONACCI RATIO RELATIONSHIPS 

Multiplicative 

.618 x .618 = .382 

.382 x .618 = .236 

.236 x .618 = .146 

.146 x .618 = .090, etc. 

Additive 

1.000 - .618 = .382 

.618 - .382 = .236 

.382 - .236 = .146 

.236 - .146 = .090, etc. 

These properties of the Fibonacci ratio are also 

true with regard to the inverse of phi, 1.618: 

Multiplicative 

1.618 x 1.618 = 2.618 

2.618 x 1.618 = 4.236 

4.236 x 1.618 = 6.854, etc. 

Additive 

1.000 + 1.618 = 2.618 

1.618 + 2.618 = 4.236 

2.618 + 4.236 = 6.854, etc. 

Once you understand these tables, you will quickly 

see why all Fibonacci multiples and retracements can 

be obtained with the PRC without ever changing the 

setting. As a matter of fact, the most common multiples 

and retracements which are found in everyday markets 

can be marked on your charts in a matter of seconds 

after a bit of practice with the PRC. Simply set the center 

guide at GS on the right-hand scale and use the compass 

as described in the section beginning on page 26. 

25


Contracting Fibonacci Ratios 

(for “Retracements”) 

Use the wide end of the PRC (points C and D) to 

measure the vertical distance of the move for which you 

desire Fibonacci retracements points. See Figure 10a 

Figure 10a 

Step #1) For .618 retracements: Keeping CD fixed, flip 

the compass. Now, AB is a .618 retracement of your original 

distance. Measure from the top down and mark this 

point W. See Figure 10b. 

Figure 10b 

26


Step #2) For .382 retracements: Keeping the PRC fixed, 

measure from the bottom up and mark a second point, X. 

The remaining length is a .382 retracement of your original 

distance. See Figure 10c. 

Figure 10c 

Set #3) For .236 retracements: Contract the PRC, placing 

compass points A and B on points W and X. This 

length is a .236 retracement of your original distance. 

Keeping the PRC fixed, measure from the top down and 

mark point Y. See Figure 10d. 

Figure 10d 

27


Step #4) For .146 retracements: Contract the PRC, 

placing compass points A and B on points X and Y. 

This length is a .146 retracement of your original 

distance. Keeping the PRC fixed, measure from the top 

down and mark point Z. 

Thus, in four quick steps, you have marked all the 

important retracements of your original distance, CD. See 

Figure 10e. 

Figure 10e 

The above directions are applicable to 

retracements of a rally. For retracements of a decline, of 

course, you must measure from the bottom up in Steps 

#1, 3 and 4, and from the top down in Step #2. 

Once you become adept at using the PRC, there 

are even more shortcuts possible. For example, if you 

want only a .382 retracement, Step #2 works independently. 

If you want only a .236 retracement, follow Step 

#2, flip the compass, and contract it so that its points fit 

the .382 span. Flip the compass again. Now, AB is a .236 

retracement of your original distance. 

28


Let’s apply this method to our textbook graph: 

.618 

Sample Objective: You wish to mark the level of a .618 

retracement of wave 1 as an estimate for the low of wave 

2. Refer to Step #1 and Figure 11. 

Example: wave 2 = .618 x wave 1 

Figure 11 

.382 


retracement of wave 3 as an estimate for the low of wave 

4. Refer to Step #2 and Figure 12. 

Example: wave 4 = .382 x wave 3 

Figure 12 

29


.236 


retracement of wave (1) as an estimate for the low of 

wave (2). Refer to Steps #2-3 and Figure 13. 

Example: wave (2) = .236 x wave (1) 

Figure 13 

.146 


retracement of wave (3) as an estimate for the low of 

wave (4). Refer to steps #2-4 and Figure 14. 

Example: wave (4) = .146 x wave (3) 

Figure 14 

30


Expanding Fibonacci Ratios 

(for “Multiples” and extensions) 

Use the narrow end of the PRC (points A and B) 

to measure the vertical distance of the move for which 

you desire Fibonacci multiples. 

Step 1) For 1.618 multiples: Flip the compass, keeping 

the spread fixed. CD now measures 1.618 times the original 

distance. Place point C on the chart at the point from 

which you wish to project a longer wave. Place point D 

vertically above or below it. Make a small mark where 

point D touches the paper. See Figure 15. 

Figure 15 

31


Step 2) For 2.618 multiples: After following the above 

steps, flip and expand the PRC so that the narrow end 

fits the 1.618 multiple distance. Now, CD = 2.618 times 

your original distance. Flip the compass again and mark 

the 2.618 multiple. See Figure 16. 

Step 3) For 4.236 multiples: The sum of the 1.618 and 

2.618 multiples yields 4.236 times the original distance. 

Just flip the compass and add AB (which is now the 1.618 

multiple length) to the 2.618 multiple distance. See 

Figure 16. 

Figure 16 

Let’s again apply this method to our textbook graph: 

32


1.618 


multiple of wave (1) as an estimate for the length of wave 

(3). Refer to Step #1 and Figure 17. 

Example: wave (3) = 1.618 x wave (1) 

Figure 17 

2.618 


multiple of wave 1 as an estimate for the length of wave 

3. Refer to Steps #1-2 and Figure 18. 

Example: wave 3 = 2.618 x wave 1 

Figure 18 

33


4.236 

Sample Objective: You wish to corroborate your 

preferred count by finding additional internal 

Fibonacci relationships between waves. Refer to Steps 

#1-3 and Figure 19. 

Example: wave 3 = 4.236 x wave 2 

Figure 19 

Smaller or larger multiples can be obtained 

with the PRC by adding or subtracting multiples of 

first generation ratios. For example, .236 - .146 = .090, 

while 2.618 + 4.236 = 6.854. Note: While these 

methods can be followed infinitely, we have found 

little evidence that the extremely large or extremely 

small Fibonacci ratios are of any practical value. 

34


A COMPLETE LIST OF KNOWN RELIABLE 

RELATIONSHIPS WITHIN PATTERNS 

developed by 

R.N. ELLIOTT and R.R. PRECHTER, JR. 

The following pages list the most common and 

useful Fibonacci ratio relationships in markets. 

IMPULSE WAVES 

Fifth Waves When Wave Three is Extended 

(see Figure 20) 

The most common multiple is 1.00 times the length 

of wave 1. Transfer the fixed length of wave 1 to the end 

of wave 4 to project the end of wave 5. 

The next most common multiple is .618 times the 

length of wave 1. Follow Step #1 under “Retracements” 

on page 26 to project this target. 

The next most common multiple is 1.618 times 

the length of wave 1. Follow Step #1 under “Multiples” 

on page 31 to project this target. 

Extensions in First or Fifth Waves 

(see Figure 20) 

By far the most common multiple for the 

extended wave is 1.618 times the net price advance 

of the other two impulse waves. Thus, when wave 5 is 

extended, the most common multiple for its length is 

1.618 times the length of wave 1 through wave 3. 

Similarly, when wave 1 is extended, the most common 

multiple for its length is 1.618 times the length 

of waves 3 through 5. Follow Step #1 under “Multiples” 

to project this target. 

35


Figure 20 

CORRECTIVE WAVES 

Zigzag Corrections 

The most common retracement is 61.8% of the 

previous impulse wave and is most likely when the 

correction itself is in the “wave 2” position. Follow 

Step #1 under “Retracements” to project this target. 

See Figure 21. 

Figure 21 

36


The next most common retracement is 50%. See 

page 22 to project this target. 

The least common retracement is 38.2%. Follow 

Step #2 under “Retracements” to project this target. 

Figure 22 

B Waves in Zigzags 

(See Figure 22) 

The most common retracement of wave A is 

38.2%. Follow Step #2 under “Retracements” to project 

this target. 

The next most common retracement is 61.8% of 

wave A. Follow Step #1 under “Retracements” to project 

this target. 

The next most common retracement is 50%. See 

page 22 to project this target. 

These same relationships also apply in regard to 

X waves as retracements of first or second zigzags in a 

double or triple zigzag formation. (See Figure 23). 

37


Figure 23 

C Waves in Zigzags 


By far the most common multiple is 1.00 times 

the length of wave A. Transfer the fixed length for wave 

A to the end of wave B to project the end of wave C. 


the length of A. Follow step #1 under “multiples” to 

project this target. 

The least common multiple is .618 times the length 

of A. Follow Step #1 under “Retracements” to project 

this target. 

These same relationships apply to second zigzags 

relative to first zigzags in a double zigzag pattern. 

Flat and Irregular Corrections 

By far the most common retracement is 38.2% of 

the previous impulse wave. Follow Step #2 under 

“Retracements” to project this target. See Figure 24. 

38


Figure 24 

Figure 25 

The next most common retracement is 23.6%. 

Follow Steps #2-3 under “Retracements” to project this 

target. 

The least common retracements are 50% and 

61.8%, which occur only when the correction itself is in 

the wave B or wave 2 position. See page 22 or follow 

Step #1 under “Retracements” respectively to project 

these targets. 

B Waves in Flats 

The only retracement is 100% of the preceding A 

wave. Expect wave B to end at the same level from which 

wave A began. See Figure 25. 

39


C Waves in Flats 

By far the most common multiple is just over 1.00 

times the length of A. Transfer the fixed length for wave 

A to the end of wave B to project the end of wave C. 

Then look for the market to turn slightly beyond that point. 

See Figure 25. 

Figure 26 

B Waves in Irregular Corrections 

The most reliable multiple with respect to irregular 

corrections is the relationship between the lengths of 

waves A and C (see Figure 26). However, often B waves 

will fit one of these two cases: 

The most common Fibonacci multiple for the 

length of wave B is 1.236 times the preceding A wave. 

Follow Steps #2-3 under “Retracements” and add this 

length to the beginning of wave A to project a 1.236 

multiple. 

40


The next most common Fibonacci multiple is 

1.382 times the preceding A wave. Follow Step #2 under 

“Retracements” and add this length to the beginning of 

wave A to project a 1.382 multiple. 

C Waves in Irregular Corrections 

By far the most common multiple is 1.618 times 

the length of wave A. Follow Step #1 under “Multiples” 

to project this target. See Figure 26. 


the length of A. Follow Steps #1-2 under “Multiples” to 

project this target. 

Figure 27 

Figure 28 

Subwaves in Double and Triple Threes 

(See Figures 27, 28) 

The most common relationship is that each “three” 

is 1.00 times the length of the adjacent “threes.” Expect 

the second and third three each to end just beyond the 

level at which the first “three” ended. 

41


The next most common relationship is that 

alternate “threes” are related by 1.618. Follow Step 

#1 under “Multiples” to project this target. 

The least common relationship is that adjacent 

“threes” are related by 1.618. Follow Step #1 under 

“Multiples” to project this target. 

Figure 29 

Subwaves in Contracting, Ascending 

and Descending Triangles 


The most common relationship is that each 

subwave is .618 times the length of the previous 

alternate subwave, i.e., wave e = .618 x wave c = 

.382 x wave a; wave d = .618 x wave b. Follow Step #1 

under “Retracements” to project these targets. 

The next most common relationship is that each 

subwave is .618 times the length of the previous 

adjacent subwave, i.e., wave e = .618 x wave d = .382 

x wave c = .236 x wave b = .146 x wave a. Follow 

Step #1 under “Retracements” to project these targets. 

42


Figure 30 

Subwaves in Expanding Triangles 


The most common relationship is that each 

subwave is 1.618 times the length of the previous 

alternate subwave, i.e., wave e = 1.618 x wave c = 

2.618 x wave a; wave d = 1.618 x wave b. Follow 

Step #1 under “Multiples” to project these targets. 

The next most common relationship is that each 

subwave is 1.618 times the length of the previous 

adjacent subwave, i.e., wave e = 1.618 x wave d = 

2.618 x wave c = 4.236 x wave b = 6.854 x wave a. 

Follow Step #1 under “Multiples” to project these 

targets. 

43


ADVANCED RATIO APPLICATION — 

A COMPREHENSIVE FORECASTING METHOD 

Keep in mind that all degrees of trend are always 

operating on the market at the same time. Therefore, at 

any given moment the market will be full of Fibonacci 

ratio relationships, all occurring with respect to the various 

wave degrees unfolding. It follows that points which 

are found to be in Fibonacci relationship to several 

market lengths have a greater likelihood of marking a 

turning point in the future than a point which is in 

Fibonacci relationship to only one length. 

The group-ratio approach works best when the 

guidelines of the Elliott Wave Principle are kept in mind. 

For instance, if a .618 retracement of a Primary wave 1 

by a Primary wave 2 gives a particular target, and within 

it, a 1.618 multiple of Intermediate wave (A) in an irregular 

correction gives the same target for Intermediate 

wave (C), and within that, a 1.00 multiple of Minor wave 

1 gives the same target yet again for Minor wave 5, then 

you have a most powerful argument for expecting a turn 

at that calculated price level. Figure 31 illustrates this 

example. 

Figure 31 

At the target market by the arrow, 

2 = .618 1, (C) = 1.618 (A), and 5=1 

44


If one of the above calculations were to yield 

one level, but two of them were to yield another level, 

the level supported by two calculations is more likely 

the valid one. 

Years of experience have proved this to be 

the most valid, reliable and useful approach to price 

forecasting in markets. The graph on page 21 is full 

of such confirming ratios, and serves as a good 

illustration of how markets often build an interlocking 

grid of Fibonacci relationships. 

45


REAL-TIME EXAMPLES OF 

FIBONACCI MULTIPLES AND RETRACEMENTS 

Rather than give the reader ‘doctored-up’ examples 

and charts of what might transpire with regard to 

Fibonacci multiples and retracements, we have chosen 

real-time examples of how Fibonacci relationships were 

actually applied in forecasting future market turning 

points. The following paragraphs are excerpted from past 

issues of The Elliott Wave Theorist: 

THE BOND MARKET 

November 1983 

“Now it’s time to attempt a more precise 

forecast for bond futures prices. Wave (a) in 

December futures dropped 11 3/4 points, so 

a wave (c) equivalent subtracted from the 

wave (b) peak at 73 1/2 last month projects 

a downside target of 61 3/4. It is also the 

case that alternate waves within symmetrical 

triangles are usually related by .618. As 

it happens, wave B fell 32 points. 32 x .618 

= 19 3/4 points, which should be a good 

estimate for the length of wave D. 19 3/4 

points from the peak of wave C at 80 

projects a downside target of 60 1/4. Therefore, 

the 60 1/4 - 61 3/4 area is the best 

point to be watching for the bottom of the 

current decline. This target zone fits the fact 

that futures contracts lose premium, and if 

the 10 3/8 bond projects an equivalent of 63 

on a “cash” basis, an additional point or two 

would probably be lost in the price of the 

futures contract over the time period of the 

decline.” [See Figure 32.] 

46


Figure 32 

April 3, 1984 [adjusting and confirming the 

target after (b) ended in a triangle itself] 

“...the ultimate downside target will probably 

occur nearer the point at which wave D is 

.618 times as long as wave B, which took 

place from June 1980 to September 1981 and 

traveled 32 points basis the weekly continuation 

chart. Thus, if wave D travels 19 3/4 

points, the nearby contract should bottom at 

60 1/4. In support of this target is the five 

wave (A), which indicates that a zigzag 

decline is in force from the May 1983 highs. 

Within zigzags, waves (A) and (C) are typically 

of equal length. Basis the June contract, 

47


wave (A) fell 11 points. 11 points from the 

triangle peak at 70 3/4 projects 59 3/4, 

making the 60 zone (+ or - 1/4) a point of 

strong support and a potential target. As a 

final calculation, thrusts following triangles 

usually fall approximately the distance of the 

widest part of the triangle. Based on the 

accompanying chart, that distance is 10 1/2 

points, which subtracted from the triangle 

peak gives 60 1/4 as a target.” 

June 4, 1984 

“The bond market ended a one-year decline 

on May 30, hitting the long-standing Elliott 

target of ‘59 3/4-60 1/4’ basis the nearby 

futures with a dramatic reversal off [an 

intraday] spike low at 59 1/2 on the June 

contract [closing that day at 59 31/32]. In the 

2 1/2 days following that low, bonds have 

rebounded two full points.” [See Figure 33]. 

Figure 33 

48


THE STOCK MARKET 

November 7, 1983 [See Figure 34.] 

“A break of Dow 1206 will virtually confirm 

that Primary 1 has peaked and assure a continuation 

of the decline. If 1158 is broken, the 

next point of support is 1090, which marks a 

.382 retracement of Primary 1”. 

Figure 34 

March 5, 1984 

Downside Targets 

“As the correction progresses, we should be 

able to get closer and closer to estimating 

where the final bottom will actually occur. 

Here are the calculations: 

1) Primary wave 2 will retrace .382 of 

Primary wave 1 at 1094.20. 

2) Within the ABC decline, wave C will be 

.618 times as long as wave A at 1089.19. 

June 4, 1984 [See Figures 35, 36.] 

“In terms of price, the downside target of 1090 

was first computed seven months ago in the 

November 7, 1983 issue. That basic target was 

reiterated in the March and April issues, 

49


with ‘buy’ strategy outlined (with minor 

variations) for the 1087-1099 area. The hourly 

low on May 30 was 1087.93. 

Figure 35 

The list of Fibonacci wave relationships now 

in place is so perfect as to be a compelling 

argument all by itself that a low is in the 

making. 

1) Wave (C) at 90.99 points, is .22 of a 

Dow point from being exactly .618 times as 

long as wae (A) at 146.88 points, a typical 

relationship in zigzags. 

2) Wave (B) at 35.27 points, is 1/2 point 

from being exactly .382 times as long as wave 

(C). 

3) Not only is wave (A) 1.618 times as long 

as wave (C), which is 2.618 times as long as 

wave (B), but the actual lengths are remarkably 

close to Fibonacci numbers: 146.88 

points (Fibonacci 144), 90.99 points (Fibonacci 

89), and 35.27(Fibonacci 34). 

4) Wave (A) lasted 5 weeks, wave (B) 

lasted 13 weeks, and wave (C) lasted 3 weeks, 

just as forecast in the May issue. The two 

impulse waves totaled 8 weeks. The entire 

50


correction lasted 21 weeks. Thus, the time 

lengths create the Fibonacci sequence, 3, 5, 8, 

13, 21, revealing that each time period, as 

precisely defined by their Elliott Wave 

structures, is related to each of the others by 

a Fibonacci ratio. 

5) Even the Minor moves are related 

precisely by Fibonacci ratios (see March and 

April issues). 

6) The Dow Jones Transports have 

retraced exactly 50% of their 1982-1984 

advance as of the low on May 30.” 

Figure 36 

June 24, 1984 

“Today’s slight new closing low in the Dow at 

1086.57 generated ‘sell signals’ all over Wall 

Street. However, it appears to me that, just 

like the May 30 low and the June 15 low, this 

minor decline is actually providing another 

excellent opportunity to buy. 

Based on typical Fibonacci relationships, I 

doubt that our ‘stop’ at Dow 1070 hourly 

reading will be taken out.” 

51


August 6, 1984 

“The leap out of that bottom (as if you hadn’t 

heard) has been one for the record books, and 

is powerful enough virtually to confirm that 

Primary wave 3 has begun. The first 

important level of resistance is Dow 

1290-1340.” [See Figure 37.] 

Figure 37 

52


THE GOLD MARKET 

The quotes presented below detail 5 consecutive 

forecasts, which were made in The Elliott Wave Theorist 

between November 1979 and January 1982, as follows: 

1) Gold should drop to $477. 

Outcome: Dropped to $474. 

2) Gold should rise to $710. 

Outcome: Rose to $710. 

3) Gold should drop to $388. 

Outcome: Dropped to $388. 

4) Gold should undergo a rise to new highs. 

Outcome: Short 3-month rise followed by 

renewed decline. But because of stop 

placement, the loss on the erroneous 

forecast was only $10. 

5) Gold going lower. Move back to the short side. 

Outcome: Gold dropped another $90 to $296.75. 

Here are the exact comments which appeared: 

November 18, 1979 

“London gold appears to be in its final blowoff 

rally on a long term basis. One all-important 

question, in Elliott terms, is whether the 

1967-68 rise in gold stocks was actually wave I 

of the long term gold bull market. If the true 

first wave was masked by the artifical price 

controls on gold at $34 per ounce, then we are 

witnessing the peak of the final fifth wave 

advance in gold from a true low in 1967! [For 

the time being, I will proceed under the 

assumption that only wave III is peaking.]” 

53


Figure 38 

March 9, 1980 

“Fibonacci support levels for gold are $565, 

$477 and $388. An ideal Elliott scenario for 

gold over the next year or two would be an A 

wave down to $477, forming the first 

retracement of the extended fifth wave within 

wave III. Then a strong rally would ensue 

forming wave B, followed by a declining 

wave C down to the final target of $388. The 

$388 level would correspond with a .618 

retracement of wave III and with the area of 

the previous fourth wave of lesser degree, a 

normal Elliott support level. The $388 level is 

the most reasonable target for the eventual 

end to the large wave IV correction.” [See 

Figure 38.] 

54


Figure 39 

April 6, 1980 

“Gold has since declined to a low of $474 on 

March 18.” [See Figure 39.] 

May 12, 1980 

“There is nothing to add to my expectations 

for gold. ...a .618 retracement of the decline 

to just over $700 should be the maximum 

potential of any intermediate rally.” 

July 6, 1980 

“I still feel that the $710 level is a very likely 

target for this rally.” 

55


Figure 40 

September 23, 1980 (the day of the high) 

“Gold has now hit its minimum target of $710 

per ounce London fixing. From here on out, 

I’d rather let the other guy have the profits. 

The ‘guaranteed’ part of the rise is behind us.” 

[See Figure 40.] 

56


Figure 41 

August 5, 1981 

“Yesterday the Fibonacci ratio target of $388 

per ounce computed a year and a half ago was 

satisfied quite closely, and the time zone of 

‘mid-1981,’ refined last May to ‘August 

1981,’ is upon us.” [See Figures 41, 42.] 

Figure 42 

57


September 8, 1981 

“The exact low on the COMEX nearby futures 

contract was $388.00 and the lowest price for 

a cash bullion sale was $388.00 by the Bank 

of Nova Scotia, both on the same date.” 

January 11, 1982 

“[The a-b-c rally into the September 1981 

high] in gold is indicating that a break of the 

$388 level is now extremely likely. If gold 

fixes below $380, I suggest reinstating your 

short position. The net result will be as if we 

had never exited the short side at all.” 

While most commodities’ wave structures clearly indicated 

that wave I began in 1967, some uncertainty had 

existed in bullion’s pattern due to government-imposed 

price controls. The subsequent break of the $388 level 

conclusively resolved this matter, confirming the wave 

count shown below. 

Figure 43 

58


PART III 

GANN ANALYSIS 

59


60


GANN ANALYSIS 

The PRC is ideally suited for many of the 

methods pracaticed by the late W.D. Gann. We do 

not attempt to evaluate Gann theory in this manual, 

rather to illustrate the usefulness of the PRC to those 

already convinced of the benefits of Gann analysis. 

THE GANN-BLITZ APPROACH 

Those researchers with either computers or a 

good deal of spare time may wish to explore a method 

similar to that used by Gann. Of course, the basis of 

Gann’s choice of “important numbers” is strictly numerological, 

and the long list of numbers he considered important 

leaves almost no number untouched. However, 

his idea of finding groups of such numbers to reveal highreliability 

future turning points can be applied successfully 

to Fibonacci ratios. This method is essentially a 

“shotgun” approach, in which the analyst takes every applicable 

Fibonacci ratio (2.618, 1.618, 1.00, .618, .382, 

... etc.), applies it to each discernible market swing on 

the chart, and plots every one of these points in order to 

find “clusters” which might reveal “magnets” for price 

turning points. 

This approach is not as useful as that which takes 

into account the guidelines of the Elliott Wave Principle 

(see ADVANCED RATIO APPLICATION). However, 

for those who have no desire to learn or apply the tenets 

of the Wave Principle, this exercise will certainly reveal 

price levels which are worth watching for changes in 

trend. Any single price level or time zone which were to 

come up repeatedly during a long series of Fibonacci 

calculations is one that an analyst should not fail to watch 

closely. 

61


Procedure: 

1) Choose the most recent swing in the market of the 

largest degree in which you are interested and apply all 

the functions under “USING THE COMPASS” to that 

swing. Add (and subtract) each of the results to (and from) 

both the beginning and end of that swing and of 

the preceding swing of the same degree. Lightly 

mark all resulting price levels on the chart. 

2) Choose the most recent swing of the next smaller size 

and repeat the process. 

3) Continue this process until the computations have been 

performed on the smallest applicable swing from the 

available data. 

4) Mark with heavy lines the boundaries around those 

price levels which cluster, or which appear a greater than 

average number of times in your calculations. Look for 

these areas to coincide with turning points. Experience 

shows that Fibonacci relationships are generally quite 

precise, so “clusters” should be tight where market turns 

are indeed likely. 

This method is best accomplished using a 

computer. 

SQUARING OF TIME AND PRICE 

By far the most widely used Gann approach is 

that of squaring time and price. This approach is based 

upon the concept that lines determined by certain points 

of intersection of time and price will provide support 

and resistance for future activity. Once a top or bottom 

has been identified, measure forward ‘x’ time units 

(i.e., hours, days, weeks, months, years) and up or down 

‘x’ price units (i.e., cents, dollars, points), tracing out 

the top (or bottom) and right side of a “square”. The 

diagonal of the “square”, moving forward in time is, 

in theory, significant in determining turning points in the 

62


Figure 44 

market. This line is referred to as a 1x1 line (1 time 

unit by 1 price unit). 

Other frequently drawn lines regarded by 

Gannophiles as having significance are 2x1 lines (2 time 

units by 1 price unit) and 1x2 lines (1 time unit by 2 

price units). 

An alternate method of ‘squaring’ is accomplished 

by measuring forward in time a number 

of time units equal to the number of price units 

represented by the levels of prior significant turning 

points. For example, a ‘square’ for a stock with a peak at 

$100 per share would occur at 100 hours, days, weeks, 

month, years, etc. from that peak, and allegedly indicate 

a turning point in price at that point in time. 

(Note: The method described on page 64 requires the 

use of chart paper where equal units are used for 

time and price. An alternate method is described on 

page 65 for paper with unequal units.) 

63


1x1 lines 

Procedure: Place point C at the beginning or end of the 

move from which the line will be drawn. Place point D 

forward in time at a price equivalent to point C. Keeping 

point D fixed, pivot the PRC so that point C is at a time 

equivalent to point D (above D for bottoms, below D for 

tops). Make a small mark. Connect the extreme point of 

the move to the mark, and extend the line into the future. 

You have just drawn a 1x1 (45 degree) line to your initial 

point. 

1x2 lines 

Procedure: Set the center guide at 2 on the left-hand 

scale. Place point A at the beginning or end of the move 

from which the line will be drawn. Place point B forward 

in time at a price equivalent to point A. Make a small 

mark. Flip the compass. Place point C at the mark you 

have just made. Keeping point C fixed, pivot the PRC so 

that point D is at a time equivalent to point C (above C 

for bottoms, below C for tops). Make another small mark. 

Connect the extreme point of the move to the second 

mark, and extend the line into the future. You have just 

drawn a 1x2 

2x1 lines 

Procedure: Set the center guide at 2 on the left-hand 

scale. Place point C at the beginning or end of the move 

from which the line will be drawn. Place point D forward 

in time at a price equivalent to point C. Make a 

small mark. Flip the compass. Place point A at the mark 

you have just made. Keeping point A fixed, pivot the PRC 

so that point B is at a time equivalent to point A (above A 

for bottoms, below A for tops). Make another small mark. 

Connect the extreme point of the move to the second 

mark, and extend the line into the future. You have just 

drawn a 2x1 line to your initial point. 

64


UNEQUAL CHART DIVISIONS 

For chart paper where the price units and the 

time units are not equal, Gann lines are still easily 

drawn with the PRC by adjusting the center guide on 

the PRC to correspond with the ratio of time to price 

on your chart paper. As an example, suppose your time 

units are twice the size of your price units (i.e., the 

height of paper used for 2 points is equal to the length 

of paper used for 1 day). Your objective is to draw a 

1x1 line. Set the center guide at 2 on the left-hand scale. 

Place point C at the beginning or end of the move from 

which the line will be drawn. Place point D forward in 

time at a price equivalent to point C. Make a small 

mark. Flip the compass. Place point A at the mark you 

have just made. Keeping point A fixed, pivot the PRC 

so that point B is at a time equivalent to point A (above 

A for bottoms, below A for tops). Make another small 

mark. Connect the extreme point of the move to the 

second mark, and extend the line into the future. You 

have just drawn a 1x1 line to your initial point, 

squaring time and price. For 2x1 lines, you can 

then multiply the setting chosen by 2. for 1x2 

lines, multiply the setting chosen by 1/2. This 

technique can be applied to various scales of chart 

paper by setting the center guide on the left hand 

scale at the ratio of the number of price units in a 

certain height of chart paper to the number of time 

units in the same length of chart paper. 

GANN RANGE SUBDIVISIONS 

Another Gann assertion is that certain equal 

subdivisions of any important move will provide 

levels of support and resistance for subsequent 

market action. According to Gann, many fractions 

were found to be important in this regard, with 1/4, 

1/3, 1/8, and 1/16 respectively having the most 

significance. For example, if the previous range was 

100 units, then a 1/4 subdivision would result in the 

65


conclusion that every 25 unit demarcation would 

represent a potential area of support or resistance. 

The most widely used range subdivision by Gann 

practicioners is that of eighths. The usefulness of 

the PRC to believers in this method is illustrated 

in Figure 45. 

Step 1) Set the center guide at 2. AB = .50 x CD. 

Step 2) Measure the wave length with the wide 

end of the PRC. Flip the compass. Place point A at one 

end and point B at an equivalent point in time to point A. 

Mark this point. 

Step 3) Flip and contract the PRC so that points C 

and D fit on the smaller length you have marked. Flip the 

compass again. Now AB = .25 x the original length. 

Step 4) Flip and contract the PRC so that points C 

and D fit on the smallest length you have marked. Flip 

the compass again. Now AB = .125 x the original length. 

The subdivisions can be projected into new high 

or low price territory for levels of resistance or support 

as illustrated. 

Figure 45 

66


ERRONEOUS USE OF THE COMPASS 

Some people have attempted to find value in 

measuring the physical length of waves on chart 

paper, taking into account both price and time. The 

problem with this approach lies in the fact that a 

physical length as defined above is subject to the 

time and price scales of the chart paper which is 

used, and thus a retracement or multiple will not 

transfer from one type of chart paper to another. If 

a method is to have significance, it should certainly 

not be dependent on chart scale. 

CONCLUSION 

The Precision Ratio Compass is the perfect tool 

for projecting ratio-based price and time targets in 

the financial markets. The foremost advantage is a 

tremendous saving of time, since you will not have to 

calculate price or time distances, write down figures, 

and then transfer the result to your chart. In fact, 

you won’t even have to check your records to make 

sure of exactly what the price levels at the turning 

points are. The Compass knows that when you place 

it on the chart. The second important advantage is 

that you will now have time to investigate all the 

relevant ratio relationships, not just one or two. You 

can even experiment with your own special ratio 

theories (pi multiples have been suggested). And last 

but not least, you will eliminate any possibility of 

miscalculation in hitting a wrong button on a 

calculator or reading and transferring the wrong 

number from a chart to the keys. The final result 

is a quicker and more accurate analysis, leaving you 

more time to make trades, with greater confidence 

that they’ll be based on complete and accurate 

information. 

67


ADDITIONAL CHARTS PRESENTED DURING 

CALCULATING FIBONACCI RELATIONSHIPS 

Using the PRECISION RATIO COMPASS 

68


69


70


71


72


1-770-536-0309 (outside the U.S.) 

or 1-800-336-1618 (inside the U.S.) 

73

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