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.

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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

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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

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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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