Study of Gann concept and the implementations

Turning Points in History part 1

An exploration into the structure of time.
By D.H. Van den Berghe

When we look at the world around us, we see change almost everywhere. In some places change seems to be slow, while in other parts of the world there are significant events that become turning points in the history of a country or even entire continent. We see such events every year in different parts of the world, but there is no obvious regular pattern as to when these events happen.

Various forms of astrology try to understand and predict these changes within the framework of cycles. Western astrology uses cycles based on the movement of the planets in our solar system.
Chinese forms of astrology work with fixed cycles of 9, 10, 12 and 60 years, and even longer..
Other cultures have still different systems.

And while each of these systems has merit and useful applications, none of them has been used very successfully in predicting the major turning points in a country's or region's history.

It is as if we are missing some important key. In this article I will present a method that may provide a new key, and allow us to predict upcoming changes more accurately.

Could we have predicted the fall of the Berlin Wall, or the September 11 attacks, or the Tiananmen Square massacre? All these examples and more, will be explored further on..

Gann's Square of Nine

The tool we are going to use in this study is called 'The Square of Nine' and was developed by W.D. Gann
W.D. Gann was a legendary trader in the stock markets, and he used this tool to make his predictions, which turned out to be amazingly accurate quite often. You can just google for “Gann square of nine” and you will easily find more about it. Although he did not publicly share the full details of his methods, it was known he used and studied this 'Square of Nine' intensively, and there were several copies of it in his office.

Here is a picture of such a Square of Nine:

The construction of the diagram is so easy, a child can do it.
You start with 1 in the middle and just spiral outwards, either going clockwise or counterclockwise (which doesn't matter for the use of this tool), filling up all the spaces..2, 3, 4..
In this example we stop at 361 in the lower right corner, but of course you could go on with 362 next to it , and then continue further upwards in the counterclockwise direction used here.
You can make it as large as you want, but this size is sufficient for our purposes in this article.
While this simple diagram looks like nothing very special at first sight, it does have rather unusual numerical relationships hidden in it.

For example if you start from the center 1 and go diagonally towards the bottom right corner, then you find all the squares of the odd numbers lining up:
9 = 3*3
25 = 5*5
49 = 7*7
81 = 9*9
121 = 11*11
and so on till infinity.. See that?

In the other direction, starting with the 4 above our center 1, we find all the squares of the even number lining up in direction of the top left corner.
4 = 2*2
16 = 4*4
36 = 6*6
64 = 8*8
100 = 10*10
and so on till infinity..
This is what makes this diagram unusual. Much more could be told about it, but that is beyond the scope this article.

Gann used it to study the movements in the stock markets, and what he discovered was that major events, climaxes and turning points had a strong tendency to occur at times that are in a “square relationship” to an earlier important date, event or turning point. To see what that means we have to turn to our diagram:

Suppose we have a major event in some 51st year (or day) (from where to count will be explained later). We have marked position #51 in clear orange in our diagram. Now what we do first is draw a straight line from #51 right through the center #1. This line will cross through all the years that are either conjunct or in opposition with our starting #51 event.

Then we draw a second line through the #1 center and exactly square on the first line. This line marks all the years that have a 90 degree square relationship to our starting #51. We can see that only a rather small selection of the numbers is on these lines, we have marked some with blue circles. Gann discovered that major events and changes happened much more frequently in the years that are on these lines. So, after year 51, the next major window of change would be year 59 (thus 8 years after the first major event).
Next year 67, then 75, 84, 93, 103, 113, 124, 136, 148,...
Notice how the first interval is 8 years, but expands and there is already a 12 year gap between 136 and 148.

That's what makes this system so different from any fixed length cycle.
And that could be the reason why sometimes our cycles seem to work and sometimes not.

I hope the basic approach is clear from above picture, but we have one question left before we can start using it.
How do we count the years or days? What is the starting point?
Gann himself reportedly used the Spring Equinox day as start and counted from there.
He mostly worked with daily numbers for his stock market forecasts, so that made sense.

But if we want to work on larger scale with yearly numbers, then we need some starting year.
Fortunately the Chinese astrology provides us.
In Chinese astrology it is the Yang Wood Rat year (Jia Zi) that marks the start of every new 60 year cycle. The most recent Jia Zi year was 1984, before that we had 1924.
These Jia Zi years also mark the start of a new major 20 year Period in Feng Shui.
So they are the first logical choice if we want to use Chinese astrology in combination with Gann's Square of Nine. How this works out you can see from the following examples.

Rise and fall of the Soviet Union

The October revolution in 1917 was the major event that marked the fall of the tzars and soon led to formation of the communist Soviet Union.
Year 1917 is in the cycle that started with Jia Zi year 1864. So it is year #53

In the late 1980's reforms started but it was not until 1991 that the Soviet Union was officially abolished.
Counting from 1864 cycle the year 1991 is #127
Looking in our diagram we see that #127 is exactly conjunct with the starting event #53.
So this was a year that strongly favored major change in the country.

Do Support and Resistance really work?

The Markets True Vital Signs:
Support and resistance are important indicators affecting chart patterns. Read on to see why. Should you consider support and resistance as indicators and meaningful markers in your planning of the trades? Unless you have a crystal ball and can tell definitely where the markets are going at any given time you don’t need to use support and resistance. But if you do not have a crystal ball, then you might consider them as one of the most important markers or indicators affecting your trades and want to learn all you can on how to measure, calculate, and use them.

When applying support and resistance, you can actually begin to predict general areas of market travel and many times very specific areas the market will go to or through. They will tell you how high a market may climb or fall and what levels or turning points to look for. Once you learn how to calculate them and with some paper trading practice you can predict what the markets may or may do. It is like reading the future in your charts before it happens. But what is support and resistance?

We have talked about it in other articles and I gave examples of them in my basic chart reading articles. One definition of support is that: Support will occur when an increase in demand for a commodity builds strength under a price. Like a floor. The opposite of support is resistance:
An example of this is when the selling pressure of a commodity becomes so strong that the buyers are overmatched and continuation of the market prices upward move is halted.

Gann and his magic numbers?
W. D. Gann a very famous trader of some years ago described many types of numbers that he calculated on a daily basis. He worked mainly with percentages based on the dollar and the number of months and weeks of the year. For this exercise we will use only the percentages based on the dollar. Some of his more popular numbers were:
6.25%
12.50%
18.75%
25%
33%
37.5%
50%
62.5%
75%
87.5%
and 100% with variations and combinations of these numbers.

He also wrote about the rule of 8, 9, 10 and even numbers. 20, 30, 40% etc. These last few were his whole number or round number formulas.

Fibonacci Numbers?
Another popular set of numbers are the Fibonacci percentages, these are also universal numbers that when used and applied to chart movements they can be very revealing. Commodity markets and for that matter Stocks move back and forth through these numbers with uncanny accuracy and frequency. Here are a small but a popular segment of Fibonacci percentage numbers: .236, .382, .50, .618: In the examples that I have chosen to illustrate for you is a recent trending market converting to a non trending market or what I describe as a ranging market. The market I have chosen is the Australian dollar.

Market Example Australian Dollar:

On Sept2 2003 the Australian dollar makes a low of 61.31 “Not Shown” and begins an upward climb. “To the far left of the chart.” On February18, 2004 the market makes a high of 77.65 and proceeds to decline over the course of the next few months to a bottom or low of 67.45 on May17th 2004. These two extremes which I did not show on the chart because of my printing parameters and positioning of the sample chart. You can refer to a May 2004 Australian $ chart to verify this move. The first climb took five months to make its ascent. And a 90-day time frame to make it back down to the bottom. Time is a market indicator you should be come aware of.

For this study we take the low of September 61.31 the position to the far let of the chart from a high of 77.65 February18th 2004 for a total Range of 16.34 points. This is the range of the high and low. This number will then be multiplied by the different percentages of the Gann numbers I gave earlier which produces the resulting percentages to be considered as either support or resistance. These numbers will be subtracted from the high as the market moves to a lower position, and added to the low of a market heading up, and for the sake of the example only we will round the numbers up or down to the nearest 10th such as 75.17 will be 75.20 etc.

Now look at the chart example and locate the support numbers as we move down. Locate these percentages on your chart. These support / resistance numbers can be used as target objectives or strategies, or buy and sell points or protective stop loss placements etc. It will take your personal touch to refine and define the points. You will see that the market passes through, stops at or pivots on these percentages. And virtually any market can be calculated and projected in this manor. The foreign currencies as well as many other markets and stocks lend themselves to the 10% rule which W. D. Gann often wrote about.

The Numbers:
0) Top level = 77.65
1) 12.5% level =75.70
2) 25% level = 73.60
3) 33% level =72.30
4) 37.5 level =71.50
5) 50% level =69.00
6) 62.5 level =67.00 Base support
7) 66% level = not reached
8) 75% level = not reached
9) 87.5 level = not reached
10) 100 level = not reached

Now considering what you have learned here in this very short exercise, is there a reason you should not take a few minutes to plot your support and resistance for the market you are planning to trade. This same high / Low subtraction or addition is used with virtually all chart calculations. These calculations may make all the difference between a winning and losing trade.

Back to our study. In this example you see when the market moves back up it comes in contact with previous resistance calculated from the markets earlier movements and either stops or is turned in the opposite direction. You use the same calculation methods over and over, from range to range. The difference is whether you apply your percentage point to the low of the market or subtract them from the high of the market. These same percentage numbers will be good over and over or until the market makes a new high or low. Each individual swing will also have its own set of percentage calculations for use and consideration. You can also recalculate these changing percentages within smaller ranges or cycles.

If the market stays in a ranging pattern, you can draw upper and lower trend line limits which looks like channels and swing trade the market. These markets can become very profitable when you learn to pre plan your moves and you can learn to preplan by paper trading. You can add trend lines, candlestick patterns, and other technical analysis tools then you have built a complete trading system that is all yours and it did not take a $2000.00 piece of soft ware, or a $2,400.00 workshop to learn. You can do most of these calculations with your straight edge, a hand-held calculator and a pencil, or a colored pen. I use RED for short positions and Green or Blue for long positions. Not all markets will lend themselves to perfect trend lines. But they do follow support and resistance.

Try this same chart exercise with the Fibonacci numbers. This market example gapped a number of times, so drawing trend lines would be difficult. By using another tool the 5 day 10 and 20 day moving average would have given you a reasonable signal for buy and sell points if you chose to trade this market.

There is no indicator that will tell you when the market is going to change direction especially with a market that is gapping. A good knowledge of the candle stick patterns will help in some respects. Gaps are covered in our trading manual: The commodity Trading Workbook: Some indicators will give you a good feel of when the market will change and you simply need to work with them for a while. Look over our free article about the DMI system and put several of these indicators together and see what happens. But do not mix so many together that you become disorganized or confused about their function, if that happens you forget to look closely at key aspects of a market and then you make the wrong decision.

Specific Rule:
Price always moves slower at the lower levels of a market and faster as the market gets higher.

“By Jim Mason of the Commoditydoctor.com. Please visit Jim’s website at www.commoditydoctor.com for additional trading material and resources “

W.D.Gann, Coffee, and Astrology

Written by Myles Wilson Walker

The following excerpts are from a letter that financial astrologer W.D.Gann wrote in 1954 in which he talks specifically about the planets relationship to coffee prices.He doesn't spell out the whole secret behind his timing but never the less it is very interesting and is also important as confirmation that astrology was behind his famous price and time forecasts. 1954:

March 24-Heliocentric Jupiter enters Cancer.
June 24- Heliocentric Jupiter is 120 degrees of Saturn.
April 12th Sun 60 degrees of Jupiter Geocentric.
April 13th Jupiter 135 degrees of Saturn Geocentric.
April 15th Sun 180 degrees of Neptune Geocentric.
April 16th Jupiter 60 degrees of Pluto Geocentric.
April 26th Jupiter 120 degrees of Neptune Geocentric.
April 26th Sun 180 degrees of Saturn Geocentric.

The month of April is very important.There should be great activity and wide swings in prices due to these aspects. GEOCENTRIC MAPS MOVEMENTS from low prices on coffee-- 1931 April 16th to August 7 1953- Mars has made 12 round trips.

1954 October 29- Mars will be opposite or 180 degrees from its place on April 16 1931.
1936 October 1st to to September 19th 1953- Mars made 9 round trips of 360 degrees each.
1954 Dec 9th- Mars will be 9 and a half round trips or opposite its place Oct.1 1936.
1940 May 15 to June 12 1953- Mars made 7 round trips or complete cycles.
1954 April 9th - Mars is 7 and a half cycles and is opposite its place on May 15 1940.
Due to the retrograde position of Mars it will again be 7 and a half July 7th and Aug.17
1954 or the third time in opposition to its own place which is very important. 1940
August 19 to September 15 1953- Mars had completed 7 round trips. Note low on coffee at that date.
1954 December 4th - Mars 7 and a half round trips or opposite its own place on Aug. 19
1940. If coffee starts to decline between March 22 and 24 1954 it should continue down to around April 15 when the adverse aspects of Jupiter to Saturn and the Sun to Neptune are completed.From these dates you should watch for the possibility of a rally up to April 16 1954 when Jupiter is 120 degrees of Neptune and the Sun 130 of Saturn.This might cause a quick rally followed by a sharp quick decline.

By studying all of the data outlined above and applying it to coffee you will be able to learn more about what causes changes in trend.

So there you have it, straight from W.D.Gann himself In my last article I did an astrological analysis of W.D.Ganns May Soybean chart based on the actual notations that he made on that chart.That dealt with Jupiters planetary ingress (Jupiter changing signs in the zodiac) and the price targets that this generated.Interestingly enough this same method as spelt out in my book Super Timing nailed the low on Soybeans again this year on July 9th.

In Super Timing I took all of Ganns trades that he mentioned in his last promotional booklet entitled -Why money is lost on commodities and stocks and how to make profits plus numerous other trades that I gathered from other sources.By doing this I was able to find the one common timing factor that linked all these trades plus price targets using one of W.D. Ganns calculators that I had discovered previously.I have called this the 1908 price target method named after the date that Gann said that he made his greatest discovery.

To my knowledge this is the first time that anyone has been able to unify all of Ganns
predictions using the same method.It solves his famous wheat prediction where Gann said wheat must trade at $1.20 by the close of trading on the 30th of September 1909 plus all the other price targets mentioned in The Ticker interview. It also solves the trades he made in 1954 at the end of his career on the coffee market using the same price and time method. The reason I think that his booklet Why money is lost on commodities and stocks and how to make profits was an important place to begin research on Ganns method is because it was written when he was 76 years old (one year before his death in 1955) and it was the perfect place for him to sum up what he considered to be the most important aspects of his work. Just to give you another idea of how planets can time the markets I will tell you another technique that I picked up when analyzing the sequence of trades that make up Robert Gordons great campaign in cotton from Ganns book The Tunnel thru the air.

Gann writes,

June 25th 1927.
October cotton declined to 16.80 Bought 500 October at 16.83 and 500 December at 17.15. He figured that it would run up for about thirty days.

July 25th 1927.
Sold 500 October cotton at 19.00 Sold 500 December at 19.20 Went short 500 December at 19.20. Decline followed as he expected.

To understand the reason for the timing of these trades just imagine a triangle and at each corner there is a planet.This is called a grand trine. What is happening in this case is that there are two slow planets that don't move much and they are 120 degrees apart(trine) Then a fast planet, Mercury in this case comes around so that it forms a triangle with the other planets (at the low of the market) it moves away so that there is no grand trine anymore but a month later the Sun comes around to where Mercury use to be and formsthe triangle again (at the high of the market).

This simple technique works but there is more to it than this and there were also price targets involved but everything is covered in depth in Super Timing as well the tools to do this work. As well as Ganns trades I've looked at examples from recent markets and find that the time and price target methods are still working well.To help people learn these techniques quickly I've also added a tutor that I originally wrote for the first purchasers of the book and put up as a website for them.This tutor is now at the end of the book and covers time cycles from recent S+P Soybean and Beanoil futures,these techniques can be used on every market. I havepurposely not covered any material presented elsewhere or rehashed the usual Gann knowledge that is in the public domain.

GANN'S LAW OF PRICE MOVEMENT APPLIED TO TODAY'S MARKET

By Gregory L. Meadors

As a young stockbroker, W.D. Gann already suspected that there were unseen causes, operating behind the scenes that were responsible for price movements in stocks and commodities. He liked to think that these hidden causes were part of a natural law that was secretly at work in the markets. As he acquired more knowledge and developed his theories, Gann systematized his theory of price movement and called it the "Law of Vibration".

In the Ticker Magazine1 interview Gann states, "In going over the history of markets and the great mass of related statistics, it soon becomes apparent that certain laws govern the changes and variations in the value of stocks, and there exists a periodic or cyclic law which is at the back of all these movements. I soon began to note the periodical reoccurrence of the rise and fall of stocks and commodities. This led me to conclude that natural law was the basis of market movements."

Gann believed that all successful men -- be they scientists, doctors, or businessmen, have devoted years to the study of their particular professions before attempting to practice them. Similarly, Gann spent many years in the pursuit of knowledge, leaving no stone unturned. Gann states, "After exhaustive research and investigations of the known sciences, I discovered that the "Law of Vibration" enabled me to accurately determine the exact points to which stocks or commodities should rise and fall within a given time. The working out of this law determines the cause and predicts the effect long before the Street is aware of either."

Gann concludes by stating, "If we wish to avert failure in speculations we must deal with causes. Everything in existence is based on exact proportion and perfect relationship. There is no chance in nature, because mathematical principles of the highest order lie at the foundations of all things."

What does Gann mean when he refers to the highest order, vibrations, and cycles? Some are familiar with cycles research which attempts to understand price cycles in the markets, but many times this study is ineffective because all the supposed regular time cycles are in fact irregular, occurring at varying time intervals. Since "Time" is based upon the Earth's rotation and it's cycle around the Sun, all standard time cycles have an Earth/Sun planetary base.

However, by studying other planetary cycles, we readily observe both regular (heliocentric), and irregular (geocentric) cycles. Of all the sources which Gann studied, perhaps the one who most influenced him was Pythagoras, who started a school of philosophy, and believed that an object could be understood by knowing its number vibration. Pythagoras is credited with the discovery of the Diatonic Scale, in which numbers and ratios determine the whole science of music.

Having established music as a science, consisting of exact harmonic ratios, Pythagoras then proceeded to divide all Creation, according to the law of harmonic intervals, into proportionate planes and spheres, each of which was assigned a number, tone, harmonic interval, and color.

Gann's "Law of Vibration" incorporates Pythagoras' Law of Harmonic Intervals. It is obvious that Gann drew heavily from Pythagorean mathematics, when he developed the squaring of "Price and Time", and the ratios by which highs and lows could be divided. A lesser known part of the Pythagorean System includes numbers ruling planets, and the ratios of their orbits, which are in harmonic relationships to each other. This harmonic organization of the cosmos was called the "Music of the Spheres."

While it is well known that Gann's primary market timing tool was based upon cosmic correlations, what is not understood my most Gann adherents is that Gann's Astro work was based upon empirical research, irrespective of traditional astrological doctrines. Gann makes this clear when he states, "these vibratory forces can only be known by the movements they generate on the stocks and their values in the market".

In other words, to obtain a high degree of accuracy when applying natural cycles, one must learn through empirical research which cosmic cycles and events correlate historically with particular Stocks, Indexes, or Commodities. This can only be ascertained by doing original research to discover the historical correlations!

For example, the October 19, 1987 Crash low was perfectly timed by the 84 year Uranus Cycle. Uranus reached the exact same position in the Heavens where it was on November 9, 1903, the day of the 1903 Crash low.

The 1987 Crash was preceded by the August "Harmonic Convergence", a rare planetary alignment which was widely advertised in the mass media (see Newsweek, 8/17/87). Our March 1987 forecast for a major top to occur at the New Moon on August 24th and to be followed by a 3 month correction perfectly timed the 1987 Stock Market top within one day.

FOOTNOTES:
1) Richard Wykoff's interview of W.D. Gann, in Ticker Magazine, 1909.

A Coincidence of Numbers

By Granville Cooley

In Book I “The Cycle of Mars” in the series “The PATTERNS of Gann” I told how a friend and I had put down the square of 144 on the weekly soybean chart of the late 1940 and early 1950 period as Gann had said to do. I said then that our reaction had been “So what?” Since we did not really see anything that caught our eye. Maybe you have done that and maybe you found something or maybe your reaction was the same as ours.

In Book I, I told of how I had laid out the heliocentric planets over this period with a little better luck. But I am never satisfi ed. I keep looking or PATTERNS. I want to fi nd things that make an exact fi t. My friend says I’m too exacting. He thinks I should be satisfi ed if things are within a number or two of being exact.

I have gone back to this chart many times, looking for that exact fi t. One day I took another approach and found what appears to be an exact fi t. At least there were enough of “coincidences of numbers” to make me think I had an exact fi t.

So take a look at the following workout and see what you think. Let’s put down the three important numbers on the chart. 436-the high in January, 1948 44-the low in December 1932 267-the number of weeks from January, 1948.

In my Book I, I told why the number of weeks might be 266, but since Gann had 267, let’s assume that it was not arbitrary. Let’s assume he had a reason for fi guring from that particular date. In other words, he didn’t just one day sit down and make a commentary on this period. He picked 267 weeks from the top for some reason.

He said that the square of 144 could be used for any squares we would like to make. But I put that square aside and decided to pick another. I picked the square of 49 or 7x7.Why? Because the chart we are dealing with is a weekly chart. If we lay down a square of 49, then it comes out on 49 weeks or 343 (49x7) days. And that would be a cube or 7x7x7.

You do not need to make up a square of 49 to look for the coincidences. You don’t need a computer. A hand-held calculator would be helpful, but you can do it with a piece of paper and a pencil. We don’t even have to have the chart. We can just picture it in our mind. At the top we have 436 and down under it we have 44 and on out to the right we can mark our 267 weeks. Now let’s use the square of 49 in the same way Gann told us to use the square of 144.

He subtracted the square of 144 from the top. So let’s subtract 49’s from the top, one at a time slowly and see if we can see any “coincidence of numbers.”
436-49=387, nothing there.
387-49=338, nothing there.
338-49=289, that’s the square of 17,
but doesn’t seem to mean much here. 289-49=240, yes, something here. Do you recognize it. Yes, it is 2/3 of a circle but it is also something else. It is the halfway point between the high of 436 and the low of 44 since 436+44/2=240.
240-49=191, nothing there.
191-49=142, nothing there.
142-49=93, nothing there
93-49=44, certainly something here.
We have subtracted 49 several times from the high of 436 and the result is the low.
So let’s put down the coincidences we have found so far:
(1) 240-the halfway point.
(2) the low of 44, by continually subtracting 49 from 436.

Gann put the square of 144 at the time of the 436 high and worked over, but I saw nothing there.Instead of doing that, I went over to 267 weeks and started subtracting the square of 49 from that. So let’s see if we can fi nd some other coincidence of numbers.
267-49=218. Yes right off we have found the halfway point of 436
218-49=169, another square, not much here apparently, but...
169-49=120, one-third of a circle, but not much else.
120-49=71, nothing here.
71-49=22, one half of the low of 44.

So let’s add those coincidences to the ones we already have:
(1)-240, the half-way point between 44 and 436
(2)-the low of 44, by subtracting 49’s
(3)-218, the half-way point of 436
(4)-22, the half-way point of 44

Just those coincidences alone look pretty good. But I kept looking for any others I might fi nd using the square of 49.

In his work Gann told about subtracting 360 from 436 and getting 76. We could subtract 76 from 436 and get 360. I decided to “add” 76 to 436 and I got 512! 512? Look familiar? Divide it by 8 and you get 64. Got it now? 512 is the cube of 8 or 8x8x8. Well, that’s very interesting you say but what does that have to do with the work at hand.

When we laid down the square of 49 on the weekly chart we were also counting the cube of 7 since a week has 7 days. The cube of 7 is 7x7x7 or 343. If you draw a 45 degree line down from 436 it will cross the week of 267 at 169. Or to put it another way 436-267 is 169. This coming out on a square (13x13) always intrigued me.

Remember in Gann’s discussion of the hexagon chart he mentioned that 169 was important for more reasons than one? I always wondered about that as maybe you have to. But somewhere along the way I found out one of the reasons. Let’s now subtract the cube of 7 from the cube of 8. 512-343=169! That’s right. The difference in the cube of 7 and the cube of 8 is the same as 436-267.

So there is another coincidence to add to our list.
(1)-240, the half-way point between 44 and 436
(2)-the low of 44, by subtracting 49’s
(3)-218, the half-way point of 436
(4)-22, the half-way point of 44
(5)-The 45 degree angle from 436 crosses the week of 267 at 169 which is also the difference in the cube of 7 and the cube of 8.

But I wasn’t done looking yet. You know me. Always adding, subtracting numbers, etc. I decided to “add” 267 to 436 and I got 703. To you that might not mean too much but it stuck out like a sore thumb to me. 703 is the triangle of 37. Look it up and see where it falls on the Square of Nine chart. It is also a Teleois angle (the book on that is in the works).

Now subtract 343 (the cube of 7) from 703 and you get 360! So let’s add those coincidences to our list.
(1)-240, the half-way point between 44 and 436
(2)-the low of 44, by subtracting 49’s
(3)-218, the half-way point of 436
(4)-22, the half-way point of 44
(5)-The 45 degree angle from 436 crosses the week of 267 at 169 which is also the difference in the cube of 7 and the cube of 8.
(6)-Adding 267 to 436 is 703, the triangle of 37.
(7)-Subtracting 343 from 703 is 360.

And now for some more.
When I added 76 to 436 and got 512, the cube of 8, I found that 436 was the “arithmetic mean” between 360 and the cube of 8 since 360 plus 76 is 436. (The arithmetic and geometric means were discussed in Book IV-”On the Square.”) The difference in 343, the cube of 7, and 267 is 76.

The number of weeks from the high of 436 to the low of 202 was 56 weeks. And for those of you who read Book IV you will recognize that as the geometric mean between the square of 7 and the square of 8 since 7x8 is 56.

In my book “On the Square” I showed where some prices were the differences in squares. We can see that the difference in 436 and 44 is a difference in several squares of 7. The difference is also equal to two squares, two squares of 14 since 14x14 is 196 and two times 196 is 392 and 436-44 is 392.

Now let’s add those coincidences to our list.
(1)-240, the half-way point between 44 and 436
(2)-the low of 44, by subtracting 49’s
(3)-218, the half-way point of 436
(4)-22, the half-way point of 44
(5)-The 45 degree angle from 436 crosses the week of 267 at 169 which is also the difference in the cube of 7 and the cube of 8.
(6)-Adding 267 to 436 is 703, the triangle of 37.
(7)-Subtracting 343 from 703 is 360.
(8)-436 is the arithmetic mean between 360 and the cube of 8.
(9)-76 is the difference in the cube of 7 and 267.
(10) From the high in January, 1948 to the low in February of 1949 is 56 weeks and 56 is the geometric mean between the square of 7 and the square of 8.
(11)436-44 is 392 which equals the sum of two squares of 14.

There are 11 coincidences in numbers we found with our original three numbers. What does it mean and how can they be used? Frankly I don’t know. But it sure cries for more study!

OK, want some more!
The difference in the cube of 7 (343) and the cube of 5 (125) is 218! The halfway point from 436.
In other words if we had an overlay with the cubes marked on it, when we put the cube of 7 (343) on 436, the cube of 5 (125) would fall on 218.
Where would the end of our overlay fall? Since 436 minus 343 is 93, the end of the overlay would fall on 93. Is the number 93 signifi cant? Why don’t you subtract 44 from it. You get 49!

Granville Cooley is author of the new book “The Patterns of Gann” available from TradersWorld. 800-288-4266

Time and Price

By Howard Arrington

William D. Gann (1878-1955) was a legendary trader who designed several unique techniques for analyzing price charts. He developed a unique combination of precise mathematical and geometric principles which are not easy to grasp. Gann analysts have spent years pouring over old charts and writings in search of Gann’s secret, and there is no end to the number of people who claim to have discovered Gann’s insight and technique that has eluded everyone else. Perhaps someone has discovered it. I am not in a position to appraise all the claims because I am not a Gann expert and have not read Gann’s writings.

Don Hall has published a book and developed a system called Pyrapoint which seems to me to be well founded in Gann principles. The purpose of this article is to take one idea used in Don’s work, and present it from a different approach, and yet arrive at the same useful conclusion. I hope even Don will fi nd my article to be an original insight to substantiate the validity of his work.

Gann’s geometric angles are trend lines drawn from prominent tops or bottoms at certain angles. The most important angle is 45 degrees, which means the line’s slope is one unit of price per unit of time. (Note: Depending of the chart scale used, the line may or may not appear to be plotted at a 45 degree angle.) For years, I thought this is what Gann analysts meant by the phrase ‘squaring time and price.’ However, Don’s Pyrapoint method gave me a new insight, which is:
Price = Time squared or P = t ^ 2

Let me take this mathematical relationship and develop it in this article. The above relationship between price and time can be plotted on a chart as shown in this illustration. The time values of 10, 20, and 30 are marked by the three arrows. See Figure 1.

For the sake of illustration, let’s suppose a prominent top or bottom occurs at a price of 400. The theory is that this signifi cant point has a mathematical counterpart. Start a new time curve at this point in time, and it will give us an expectation for a future top or bottom to occur on this curve. This principle can be stated as ‘When price meets time, a change is imminent.’ This ‘price meets time’ relationship is shown in the following chart. See Figure 2.

With the prominent top or bottom at P, if price meets the curve at point A it will do so in 18 bars. The time to A is the square root of the price at A. Price at A is 324. Square root of 324 is 18.

If price meets the curve at point B, it will do so in 20 bars. The time to B is the square root of the price at B. Price at B is 400, therefore the time to B is 20 bars.

If price meets the curve at point C, it will do so in 22 bars. This is a very interesting concept!

Remember that price and time are related by the formula:
P = t ^ 2 or t = sqrt( P )

In this article, I will develop the mathematics for the slope of a trend line using the price and time relationship presented in the previous article. Let’s work with the model illustrated in this See Figure 3.

From the previous article, the next time curve will be t bars away for a given price P. At a time t+1 price would meet the curve at price P1. Now, lets solve for the slope of the trend line shown in blue which connects P and P1.

P = t ^ 2

P1 = (t + 1) ^ 2 = t ^ 2 + 2 t + 1 = P + 2 t + 1

Slope = (Change in price) / (Change in time)

Change in price = P1 - P = P + 2 t + 1 - P = 2 t + 1 = 2 t + 2 - 1 = 2 [ t + 1] -1

Change in time = t + 1

Therefore, slope of P to P1 is = (2 [ t + 1] - 1) / (t+1) = 2 – 1 / (t+1) = 2 - 1 / sqrt( P1 )

If we normalize all prices to consider three signifi cant digits, then all prices will fall in the range
of [100 ... 1000]. By substituting the price boundaries into the slope formula,
we can get a range of slopes as follows.

For a P1 of 100, the slope of the up trend line to 100 = 2 - 1 / 10 = 1.9
For a P1 of 1000, the slope of the up trend line to 1000 = 2 - 1 / 100 = 1.99
The slope of the up trend line at the midpoint of this price range is 2 - 1 / sqrt(500) = 1.96

Let’s call this trend line a 45 degree line because we developed the slope using one unit of price change from P to P1 with one unit of time t. For this 45 degree line, the slope is basically 2. I
think this is strong justifi cation as to why Gann used 2 cents as the price grid interval of his daily grain charts. Such a scale layout would naturally give Gann 45 degree angles with a slope of 2 cents per daily bar. I have shown that 2 is the slope of the upward 45 degree trend
line that develops from the price and time relationship given by the formula: P = t ^ 2.

One can solve for the slope of the downward trend line from P1 to P to obtain this result:

Slope of P1 to P = (-2 t - 1) / (t-1) = (-2 [t - 1] - 3 ) / (t-1) = -2 - 3 / (t-1) = -2 – 3 / (sqrt( P ) - 1)

For a P of 100, the slope of the down trend line to 100 = -2 - 3/9 = -2.33

For a P of 1000, the slope of the down trend line to 1000 = -2 - 3/99 = -2.03

Again, the slope of the down trend line approaches a value of -2. Therefore, -2 is a good approximation for the slope of a downward 45 degree trend line.

Now I would not bother to give you the mathematics in the previous two articles if I did not fi nd application of this theory in the charts. I used the mathematics given in the fi rst two articles to
develop a tool in ESPL which draws horizontal lines at calculated price levels, and nearly vertical time curves at the calculated time intervals. This forms a grid of trapezoids like the previous illustration. (Don Hall calls them ‘squares’.)

Diagonal lines connect the corners of the trapezoids to give support and resistance trend lines.
Here is a daily chart of JNPR with the construction started on the highest high. All price levels, time intervals, and trend lines are constructed mathematically from two pieces of information: the price $244.50 on the date 10-16-2000.

There is more in this chart than I have space to explain. But, I can point out some haracteristics. The horizontal price lines have a label on the left which is a degree of rotation around a Square of 9. This is covered in the Pyrapoint book, but is beyond the scope of this article. Note that in my example, the time lines are nearly vertical. This is a slight variation from the method of construction in the Pyrapoint book which shows vertical lines. I feel that my presentation is appropriate because of the theory of the time curve illustrated in my fi rst article. The time curve forms the left and right sides of the trapezoid, and the price levels form the top and bottom sides.

Time: Time is measured by the time curve, which is related to price.
Tip: ‘As price meets time, a change is imminent.’
Note the first time line labeled 12 on the bottom and 16 on the top.
If price meets time at the -720 horizontal, then the time for the change would be the 12th bar from the top.
If price meets time at the -540 horizontal, then the time for the change would be the 13th bar from the top. At the -360 horizontal, the time change would be in the 14th bar. At the -180 horizontal, the time change would be in the 15th bar. At the 0 line, the time measured would be 16 bars.

That is why the top of the time line is labeled with a 16, and the bottom of the line is labeled with a 12. Starting at 16, for each 180 degree down the time count is reduced by one bar, or for every 180 degree rise, the time count increases another bar. Note that the market did experience a change when price met the time curve labeled 12 to 16!

The price at the 12 to 16 time line was used to obtain a forecast of the 2nd time line, which is labeled 25 to 31. As the price meets each time curve, a new time curve is calculated based on the price. Each of the time curves shows excellent correlation with market change when price met the time line.

Prices: The prominent high of $24.50 is the calculation basis for all the horizontal price levels that are shown.

Tip: The market seeks out these price levels, and you can calculate these prices in advance. Note how the market fell to the -540 horizontal, rallied to the -180 horizontal, fell to the -900 level, rallied to the -540 level, fell to the -1080 level, and rallied to the -720 level.

Trend Lines: The downward 45 degree trend lines shown in red create a flow channel, or ‘price highway’ as Don calls it.
The upward 45 degree trend lines shown in green create a price highway going the other direction.
The red lines are resistance lines that the market must close above to change direction from bearish to bullish.
The green lines are support lines that the market must close below to change direction from bullish to bearish.

We all have used upward trend lines placed underneath action lows to indicate support, and downward trend lines placed above action highs to indicate resistance. The beauty of this tool is that these diagonal trend lines are computed in advance, and the market seems to have respect for them. Price fl ows up and down the channels. The more you study the example, the more impressed I think you will be with this tool.

The Pyrapoint tool can also be applied to intra-day charts with good success. The size of the price interval used on a daily chart seems to be too big for use on an intra-day chart. No problem. Don points out that there are squares within a square. All one needs to do is subdivided the price interval into halves, fourths, or eighths. The time interval is determined from price and will not change.

One question that I have dealt with is this: If the time interval computes to be 11 bars because the price is at 121, which intra-day bar time frame should I use? If 1-minute bars are used, then we have a time curve 11 minutes later. If 2-minute bars are used, then the time curve would be 22 minutes later. If 5-minute bars are used, then the time curve is plotted 55 minutes later. Now do you see why I have a question? The selection of the intra-day bar time frame greatly affects the time interval measured by the next time curve.

Here is how I tackled the problem, and the proposed solution. I displayed a 1-minute chart and used a cycle tool to measure in hindsight the cycle rhythm from bottoms to bottoms, tops to tops,
and/or bottoms to tops. When I found a cycle width that seems to fi t by catching multiple turning points, I note the number of minutes in the cycle. I use this formula to estimate a good intra-day time frame to use.

Intra-day Bar Time Frame = Cycle width in minutes / sqrt( P )
Example: On the JNPR 1-minute chart I found a 65 minute cycle when the price was around $133. Therefore, bar time = 65 / sqrt( 133 ) = 5.6 minutes per bar. So, using a 6-minute chart, or
possibly a 5-minute chart should show a good fi t with the Pyrapoint tool. I happened
to have been following a 5-minute chart, and I do fi nd excellent correlation.
I have used a smaller price interval by subdividing the 180 degree interval into
eighths in this example. See Figure 5.

Please study the chart, and observe the fl ow of prices in the up and down trend channels. Note how trend changes occur on or near the vertical time curves, and how the market seeks the horizontal price levels. This entire road map is computed in advance from the prominent
top that occurred on January 12th at 9:35 a.m.

Mr. Arrington can be reached at Ensign Software, www.ensignsoftware.com. This article came from thier technical newsletter. If you are interested in the Pyrapoint System. You can purchase the Pyrapoint Book with the script and demo program on CD for just $179.95. + shipping. Call 800-288-4266 or go to www.tradersworld.com

Something is Wrong With Gann Angles

By Ken Turkin
When we measure a correctly drawn 1x4 line with a protractor or use the tangent function on a calculator, we get 14.03 degrees. Gann said it was 15 degrees. A 1x2 line is 26.56 degrees yet called 26.25. Everyone just copies Gann’s numbers, but couldn’t he just as easily have said the 1x2 was 26.5 and the 1x4 was 14 degrees. Why the discrepancy, couldn’t Gann count?

Gann’s geometric angles are proportional parts of the 360 degree circle and used to measure time and space. The circle and the unique numbers of 1 thru 9 were the basis for all his calculations.

Using fi xed rate of movement trendlines is an easy way to measure this relationship of price to time. It is because of this convenience, there are slight variations in the numbers. To find the various Gann angles, on a properly scaled chart, all we do is count the squares up and over. These angles measure the ratio of how much price has moved in a specifi c time. For example a $5 move in 20 days, has the ratio of 5 to 20 and equal to a 1x4 line. We can use different proportions such as the following:

Angle Price units Time units Gann Angles
1 x 4 1 4 15.0
1 x 2 1 2 26.25
1 x 1 1 1 45.0
2 x 1 2 1 63.75

On the chart below, one quarter of a circle, 90 degrees, is drawn on a 12 by 12 square background grid. This circular arc is also divided in 24 even parts of 3.75 degrees each. The 90 degree angle is used, because it is the strongest. It is vertical, straight up and down like the sun at noontime. The trigonomic proportions of sine, cosine and tangent for the first 90 degrees are unique. Then they are mirrored and repeated for the rest of the circle sometimes with their signs reversed depending on which circle quadrant they are in.

From the lower left corner starting point on the chart, 4 lines are drawn thru the arc and extended to the square’s perimeter. Counting the number of squares shown will give the correct Gann angle line and their actual calculated degrees using the Tangent function, or more correctly the ArcTangent from a calculator.
Angle Price Time ArcTan
1 x 4 3 12 14.03
1 x 2 6 12 26.56
1 x 1 12 12 45.0
2 x 1 12 6 63.43

It is easier to count squares or have our computers use the tangent function. Although the results are close to true Gann angles, they would be more suited if we were measuring on a square grid. But Gann did just as he always said and was thinking in proportionate parts of the circle. In this case 90 degrees is divided into 24 parts of 3.75 degrees each as shown by the 24 lines hitting the circles circumference. You can see how close the 4 extended lines are to them. That is the difference. The 1x4 Gann angle of 15 degrees is the 4th line on the circle (4 times 3.75 = 15) and just above the 1x4 tangent line of 14.03. The 1x2 line is the 7th line and the 2x1 is the 17th line on the circle. Both lines come out equal at 45 degrees, the tangent is 1 and 12 times 3.75 = 45.

Gann was a master mathematician, who knew the difference between convenience and hard work, with enough fi ngers and toes to count correctly from 1 to 9 and beyond. He also counted on human nature not changing, to supposedly hide some of his secrets in the best place possible - right in front of our face. Although this topic was a minor unquestioned nuance, it is our assumptions and perspectives that helps perpetuate the mystique.

Here are a few related observations. If we had used a background grid of 17x17, or 289 small squares (very close to 144 times 2), the upward 1x1 line hits the circle almost perfectly at 12 lines up and 12 over. Since dividing squares into eighths is common, and so is the 8x8 to an inch paper scaling, then using 90 degrees as the basis each eighth would be 11.25 degrees or 3 times 3.75 degrees. Even the diagonal on an 8x8 square measures 11.3 units which is also close to 11.25.

One last angle would be to draw the 2 diagonals (the 1x1 lines up and down) on any square. This will create 4 triangles. Using the idea that if price is above a 45 degree line (1x1) it is strong and below it is weak, then only the upper triangle is always strong and the lower triangle is always weak.

Gann always talked about squaring price with time. With that area he added volume, trading activity was not to be taken lightly, but in depth. These points of balance would then help defi ne a markets larger solid structure. Squaring the circle was of great interest, to harmonically bringing the heavens down to earth or maybe coordinating the rectangular to polar. With “use all my rules” his measurements in and out, ruled over what was always here and is here, before us.

So obviously, Gann could count, but I wonder why he couldn’t write right!
Ken Turkin can be reached at MarkeTree@aol.com

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