Gann's Use of the Square of 9

[RichardCox 10]

W.D. Gann is one of the most well-known contributors to the field of technical price analysis and this is due, in large part, to the unique approach he took when forecasting potential price direction. Gann’s decision to take some time away from trading and actually study the way market prices behave should be seen as a model of practice in itself but there are many traders that are highly skeptical of some of Gann’s underlying ideas.

 

Here, we will look at Gann’s interpretation of the Square of 9 as it describes the distribution of prime numbers and then price forecasting. More widely known by mathematicians as Ulam’s Prime Number Spiral, the Square of 9 does receive criticism over the mystical nature of the analysis, and its seemingly disconnected relationship to the financial markets. First, we look at how the Square itself is constructed.

 

Constructing the Square

 

When looking at Gann's Square of 9, integers are arranged as a square, and can be constructed using graph paper by placing “1” in the centermost box, placing “2” on the box to the left, placing “3” in the box above. Then, we move clockwise and add consecutive numbers: “4” is placed to the right of “3,” “5” is next, and “6” placed below “5.” When we reach “9” the first square is completed, and “10” will start the next square. This can be seen in the first attached graphic.

 

According to Gann, this collection of numbers is composed of a hidden rules that can be applied to the financial markets. For Gann, these numbers can be viewed as prices, and their progression as a circle can be viewed as the sequence of time. The completion of one spiral will lead the trader to the next spiral, and this will also represent the completion of one time period (for example, a day or a year).

 

Of course, some numbers in these diagrams are more important than others, and those in lines that fall on the 8 directional lines found on a compass are considered to be more significant. When looking at the northern, eastern, western, and southern “compass lines” traders can see the areas where prices will align at certain periods within the unit of time you are watching. This can also be seen in the northeastern, northwestern, southeastern, and southwestern compass lines as well.

 

Identifying Support and Resistance Levels

 

So, in essence, these lines fall as a “cross” and an “X” in the number arrangement. Once these areas are identified, traders can watch for prices to hit a major high or low. So, for a frame of reference, if prices hit a high of 85, you would expect prices to find support at 52 because this is the next number in line as you move toward the center of the square. But how, exactly, are these numbers determined?

 

The calculations for these numbers are relatively simple, as we take the larger number (85), and find its square root (9.2). We then subtract 2 (giving us 7.2) and then square this number, giving us the next sequential number toward the center. When moving in the opposite direction on the square (finding resistance), you will reverse the operation and then add 2 to the square root (rather than subtracting 2).

 

Angular Relationships

 

When trading with Gann theory, we look price relationships by marked by angles of 180 degrees, 90 degrees, etc. The relationship between 3 and 9, for example, would be 90 degrees, where the relationship between 3 and 7 would be 180 degrees. With this information, investors can forecast the magnitude of potential price oscillations and this can allow traders to time major reversals in price activity.

 

To be sure, Ulam’s Prime Number Spiral has some very different applications in the world of mathematics. But Ulam noticed that when constructing this square, sets of prime numbers could be found in diagonal lines within the wider diagram. These prime numbers can be seen in grey in the larger diagram attached. As you can see, prime sequences (such as 81, 131, 181, and 239) start to become apparent.

 

These patterns continue even when the square is stretched to much larger parameters. In the 45 degree angle from the center, 70% of these fields will show primary numbers (much higher than the 20% of the sequential integers which are actually prime). In terms of mathematics, this is viewed as significant because prime numbers can be thought of as the natural “elements” of all other numbers in that they are calculated by multiplying primary numbers together.

 

Parabolic Shifts

 

For this reason, the angular distribution of these numbers is a much-discussed mathematical mystery. According to Gann, these patterns mark evidence of underlying mathematical order that can be applied to other arenas and create trading opportunities for those in forecasting future price movements. The Square of 9 is, in essence, a parabola calculator and each angular ray from the center can be expressed as a quadratic equation, so when looking at a price and time chart, parabolic curves are formed. Gann’s argument is that prices falling along the same angles “vibrate” together along a parabola.

 

In some sense, this should be relatively unsurprising, given that prices are vulnerable to large retracements when momentum goes parabolic. Parabolas can also be thought of as slowdowns and reversals in trends, so when looking at Gann’s structural elements in this light, applications to trading the financial markets start to become more visible.

 

Price and Time Relationships

 

At this stage, it should be clear that, for Gann, major tops and bottoms in prices have mathematical relationships. This cause-and-effect relationship that exists in price movements of various time periods then become the governing factor when determining how prices are likely to behave in the future. In the Square of 9 chart all forms and numbers are derived from the 9 integers that complete the first cycle. Finding the “zero point” becomes critical when determining the vibrational center that will theoretically affect prices in the future.

 

But the main thing to keep in mind is that the dates of the highs and lows are related (in addition to the price levels themselves). So, when the harmonics of both price and time square with one another, Gann theory suggests that major reversals will likely be seen. When a larger cluster of price and time harmonics is seen, the reversal is thought to be more forceful. Another important factor to remember is that smaller time frames must be used in identifying significant highs and lows (so, for example, it would not be recommended to simply use the yearly highs and lows). This is viewed as lending credibility to the projections of the cycles of price and time. All trends are made up of sub-trends which move with and against one another, so all of these factors must be considered when making Gann projections.

[SIUYA 11]

I for one thought it was bitterly disappointing when I did not implode a few seconds ago when the clock ticked through 12:12:12 on the 12-12-2012

 

(the last repetitive sequence this century so i am told) no relationship to Gann or his value.

[SunTrader 10]

........... such as 81, 131, 181, and 239 ........

 

You mean 89, 131 etc