[The following is a reprint of an article in 'The W. D. Gann Technical Review', written by Billy Jones in September 1985.]
180 DEGREE OR 180 DAY CHANGE OF TREND One of W. D. Gann's methods to determine major trend changes is the "180 Degree" or 180-calendar day trend change. 180 degrees of the cycle of a year is equal to 180 days. Gann said to watch all markets that have been up or down that period of time. Let us look at a couple of markets on this basis. The December S & P made a contract low on January 7, 1985. Gann would be watching the area of July 7, 1985 for indications of a change in trend. The high was made on July 17, 1985 which was actually 10 calendar days off but still in the ball park.
The Swiss Franc made bottom in the December contract on February 26, 1985. We would want to watch for a trend reversal in the area of August 26, 1985. The top was made on August 22, 1985. The next week we had a weekly reversal.
The December Deutsche Mark would also be included in this category of 180 degree or 180 day reversals. Most of the foreign currencies, with the exception of the Canadian Dollar, usually make tops and bottoms in unison.
Look at December Gold. Contract lows were made on February 25, 1985 and a high was made on August 19, 1985. The actual top was made on March 21. The high of August 19 was within six dollars of the actual top, a double top. The high of August 19, 1985 should be considered the "180" degree or 180 day high. Notice how many changes of trend we had in gold on or around the 21st of the month.
What about Orange Juice? It made a contract top on January 24, 1985. We should look for indications of a bottom six months later and a low was put in on July 31, 1985. I would watch this market for a signal that this is the bottom. (Double bottom, key reversals or taking out the swing top.) Incidentally, we are also reaching the time of the year for Orange Juice to make its "fall or winter frost scare" which is usually the end of November. It is always a good practice to buy O.J. futures to take advantage of the weather scare. It usually comes in December, but last year the scare came in January, and was already near contract highs. You could see a fifty point move this year. A couple of years ago this market made basically the same type of bottom formation and broke out to the upside for a 90 cent move in a very short time. The risk reward on this trade is very good. You should always watch for changes of trend at the ¼, ½and full year. This coincides with 90 days, 180 days and one full cycle of 360 degrees or the year. September 22 will be a very strong time period this year as always.
October Live Cattle have taken out their swing bottom and are pointing to lower prices. Watch the bottom of the price square for support which is in the 52.70 area and on the 45 from the top.
One of W. D. Gann's methods to determine major trend changes is the '180 Degree' or 180-calendar day trend change. 180 degrees of the cycle of a year is equal to 180 days. Gann said to watch all markets that have been up or down that period of time. Above the 180-degree or 180-day market moves of the S & P, the Swiss Franc, the Deutche Mark, Gold, Orange Juice and Live Cattle were illustrated. These examples were from the year 1985. Before examining some recent examples of 180-degree or 180-day changes of trend, let us first note what Mr. Gann taught us: MONTHLY CHANGES Stocks make important changes of trend every 30, 60, [90], 120, 150, [180], 210, 240, [270], 330 and 360 days or degrees from any important top or bottom. These seasonal changes or monthly changes based on the beginning of any seasonal changes are important to watch for tops and bottoms. (Gann, W. D., W. D. Gann Stockmarket Course, Lambert-Gann Publishing Company, Pomeroy, WA.)
The above quotation from the W. D. Gann Stockmarket Course is a very powerful statement indeed. In a few brief lines W. D. Gann outlines the basis of 'Solar Degrees' and its link to Seasonal Time. It has even greater significance if one studies the numbers he omitted (inserted in square brackets above) and relate them to the Gann symbol. At this point you may find it beneficial to re-read Volume 1, Number 4 of The New W. D. Gann Technical Review that discusses the concept of 'Seasonal Time'. Solar Degrees is a special case of Seasonal Time, where the starting point becomes a major high or low in the market, rather than the dates of the solstices or the equinoxes. Days and Degrees Days and degrees are two entirely different methods of measuring time. One day is one revolution of the earth on its axis. This is 1/365th of a calendar year. One solar degree is the time it takes for the earth to travel 1/360th of its elliptical orbit around the sun. As there are 365.24 days on one year and 360 degrees in one year, one day does not equal one degree. In the quotation above, Gann said: Stocks make important changes of trend every 30, 60, [90], 120, 150, [180], 210, 240, [270], 330 and 360 days or degrees from any important top or bottom. Note that he said days OR degrees. The following charts illustrating the concept of markets moving in 180-degree or 180-day moves:
Australian All Ordinaries SPI 200 - 178 days, low to low.
S&P 500 - 178 degrees (183 days) low to low.
Swiss Franc - 179 degrees (183 days) Solar degrees can be a powerful method of determining the likely dates of major and intermediate market tops and bottoms.
The following is reprinted from an article Billy Jones wrote in Vol. 4, No. 1, of The W. D. Gann Technical Review dated January 1985 titled '0 to 360 degrees - March 21 to March 20 - A Cycle.' It shows clearly the importance Mr. Gann attached to the 'Square of Nine Calculator':
W.D. Gann's Square of Nine The Square of Nine and the Square of Four are two of the most interesting charts in the W. D. Gann course of study. I have spent a lot of time with these charts. I was first introduced to the Square of Nine in 1972 when Ed Lambert sent me one. It was the smaller one that covers squares 1 to 33 inclusive. At the time I was just getting started in commodities and I did all kinds of crazy things with the chart in relation to my trading of wheat and cattle. Some of them worked and some of them didn't. I gradually moved away from the Square of Nine into other techniques that I had learned from the Gann course. In 1976 I went to Miami, Florida to close the deal I had made with Mr. Lambert on the purchase of Lambert-Gann and Gann's research, library, etc. While there, my interest was rekindled in the Square of Nine. While there, I saw a picture of Mr. Gann sitting at his desk and upon his desk was a model of a pyramid with the numbers, exactly like those on the Square of Nine, painted on the model. I remembered that the first thing that came to me was that I was looking down at a pyramid with the number 1 on the top and spiraling outward to the end. This picture really stuck in my mind. Gann also had a large Square of Nine printed upon a very old papyrus substance that was framed and hanging on the wall. Many of you that have been in my office have seen this large original chart. When I got all the Gann charts home in Pomeroy and started going through them, I found that Gann had actually used the chart consistently. There was one for just about every commodity and stock that he traded. They were in all sizes and were constructed for many different reasons, it appears… …The fact that there were so many different ones tells me that he was able to forecast with them. The other important fact that I have learned from the ongoing study of them is that actual market movements coincide with the layout of the charts' TIME and DEGREE cycle of 360… We will now take a look at the degree movement of price of one of Mr. Gann's most important calculators, the Square of Nine. Under the section titled 'Time and Price Resistance Points According to Squares of Numbers' in the W. D. Gann Commodity Course, Mr. Gann wrote that: Stocks [and commodities] work out to the square of different numbers, triangle points of different numbers, the squares of their bottoms, the squares of their tops, or to a halfway point of the different squares according to the time period.
Therefore it is important for you to study the resistance levels according to these numbers. The squares of each number and the halfway point between the squares of one number and the next point are very important. For example: The square of 2 is 4; the square of 3 is 9. The halfway point between 4 and 9 is 6.5. The square of 4 is 16; the square of 5 is 25. The halfway point between 16 and 25 is 20.5. The square of 6 is 36; the square of 7 is 49. The halfway point between 36 and 49 is 42.5.
The square of 8 is 64; the square of 9 is 81. The halfway point between 64 and 81 is 72.5. The square of 10 is 100; the square of 11 is 121. The halfway point between 100 and 121 is 110.5. The square of 12 is 144; the square of 13 is169. The halfway point between 144 and 169 is 132.5. If you examine closely the numbers of the 'square of nine' or the 'odds and evens chart' (see below), you find that these natural squares are aligned on the same angle from the center. The odd squares of 1, 9, 25, 49, 81, and so on, go from the center down to the lower left-hand corner. The even squares of 4, 16, 36, 64, 100, and so on, go from the center up to the top right-hand corner. Since the distance from 16 (the square or four) to 25 (the square of five) is 180 degrees around the chart, it becomes clear why Mr. Gann expected changes in the trend of a market price at 180 degrees or 'on an angle of 180'. Similarly, he would expect changes at 90 degrees (one-half of one square) and 360 degrees (two squares). The square progression seems to work better with three significant digits. If you are studying a market with four digits in a price, try dropping the last number to get to a number you can use on the chart. Similarly, if you are studying a low price stock, try adding a zero or move the decimal to get three significant digits. The square of nine is without a doubt one of Mr. Gann's most powerful trading and analysis tools. It also can be a little complex. Mr. Gann was clear in his instructions about where to expect this support and resistance to occur on the Square of Nine. If you are unclear about the angles that are important to price movement, please reread Vol. 1, No 7, which describes why the angles of 90, 180, and 360 degrees are so important. These angles show up repeatedly in Mr. Gann's writings because they describe the geometry of the square (0, 90, 180, and 360 degrees) that can then be placed inside the circle (0 to 360 degrees). Thus the esoteric term of 'squaring the circle' becomes a reality. By placing these angles on the natural squares chart from the center, one moves from one natural square to the next in 180 degrees. The midpoint between squares is reached in 90 degrees and the full circle or cycle of 360 degrees moves two full squares from its starting point. This first example is December Wheat 2002. The contract high of 319 is made early in the contract in January. In early May, the market makes the low of the contract to the date of this article at 283 ½. The square root calculation for this movement is as follows. Square root of 319 = 17.86 Square root of 283 ½is 16.84 17.86 - 16.84 = 1.02, which is within .02 of one full square
This is easily seen on the Square of Nine by finding 319 just right of the angle moving up from the center to the 12:00 o'clock position. Then 180, degrees or directly across to the bottom left, is the bottom at 283 .
The next example is of the S&P Mini electronically traded contract. This contract is setting records every month in terms of volume of trades. It is the small version of the Standard and Poor's stock index. The chart is continuous in that the four traded contract months (March, June, September, and December) are linked together when the volume in the new contract exceeds the old contract. In other words, the March contract is traded until early March when the volume in the June contract exceeds that of March. The year to date high for 2002 is January 7th, at 1178.50. The intermediate low following that high came on February 20th, at 1073.75. The market then rallied to the double top area of 1177.5 on March 19th. From there the market made a lower swing low on May 7th at 1045.75. Following the square root mathematical formulas gives us the follow calculations: Square Root of 1178.5 = 34.33 Square Root of 1073.75 = 32.77 34.33 - 32.77 = 1.56 or just .06 from moving 1.5 squares or 270 degrees The next move back up to 1177.5 is obviously 270 degrees also.
Square Root of 1177.5 = 34.31 Square Root of 1045.75 = 32.34 34.31 - 32.34 = 1.97 or just .03 from moving 2 full squares or 360 degrees. This is easily seen on the Square of Nine locating 1178 on the right side just below an angle moving from the center to the 3:00 o'clock position. The first low at located by moving 270 degrees counterclockwise to 1074. The second low of 1045 is located adjacent to the 1177 and 1178 highs.
These examples are excellent exercises in the use of a different type of mathematics to explain market movements. There is nothing strange or unusual about these markets and they certainly represent some of the most highly traded market in the world. Thus one could conclude that many market movements can be understood if we just change the methods we use to calculate those movements.
Gann Square The Gann Square of 9 is based on a concept that the number of TIME units for a 360 degree movement of price is equal to the SQUAREROOT of price at the inflection / turning point from which we wish to project the forthcoming time price relationships and that the 360 degree rotation of price is based on the above noted relationship of adding/subtracting a value to/from the squareroot of the price value at an inflection/turning point. This concept has been offered first by Gann then by Dunnigan and, recently by Don Hall.
If we take a portion of the familar Gann Square and look at the 315 or 45 degree line (depending on whether we measure Gann Angles clockwise or counterclockwise) we find the series of numbers enumerated below. To see how these numbers fit the square of nine see the above small portion of a square with brackets around the key 45/315 degree numbers. 45/315 degree line numbers: 1 9 25 49 81 121 169 225 289 361 441 529 625 729 841 961 the above numbers are the square of the following series: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 If a turn around the Gann Square of 9 is considered to be a 360 degree trip then using this relationship: 1. Given some value of price termed Price1, 2. To arrive at Price2 which is 360 degrees away from Price1, calculate: Price2 = Square(SquareRoot(Price1)+2) Example: Above square root of 81 is 9 and Above square root of 121 is 11 which is 9 plus 2 and when squared is equal to 121 so 121 is 360 degrees from 81; Therefore: Price2 = 360 degree price of Price1. That being true then the squareroot difference for Gann Angles of 180=1 and 90=0.5 , and any Gann Angle desired can be calculated from this relationship ! ! ! !
