135 90 45

0-360

0 360

Rgure 2

225 270 315 Rgure 3

computerized technical analysis you vmuld be wise to mark on the charts the points were buy and sell signals appear from that work. This will allow you to see at what price and time those occurred. After some period of time you will be able to qualify those signals better with the understanding you will develop from this analysis. Doing this will allow you to avoid the many whipsaws that are inherent to those buying and selling oscillator signals.

ANGLES

From the use of the charts which have the equal time and price relationship] Gann went on to find that certain fixed angles had a very significant relationship to price movement. The basis of the angles which Gann used came, again, from the 360 degree circle. This circle, or more specifically, one quarter of the circle or 90 degrees, is the basis of the angles.

Anyone who has studied the recurrence of events is aware that events do follow cycles, and when these cycles are viewed as circles, the relationship of time and event becomes easier to picture. The illustrations below show how the circle relates to the angles, and then further to the squares whioh are so prevalent in Ganns work. The circle is one of the basic elements of geometry, and the angles radiating from the center of the circle divide it into sections. The circle is divided into 360 degrees, with four major divisions or cardinal points within the circle, one every 90 degrees. (Figure 1)

The 90 degree angle is the basic angle of a square, and if we view it in this fashion, the square formed by the 90 degree angle in the circle appears as shown. (Figure 2)

The 45 degree angle divides the square in half and gives a further division of the circle. (Figure 3)

13 weeks

15 points

0 360 26

Rgure 4

39 weeks Rgure 5

Oor 60

45 points Figure 7

Figure 6

26 39 52

The next signifioant division of the circle is by thirds, which is referred to as trines, and the degrees represented are 120, 240, and 360, (Figure 4)

So, the counts along the chart from significant highs or lows are an indication of the time cycles in a linear manner. Ninety degrees of one year in days is then 90 days. Another way of viewing the counts is to picture Figure 3, hold the circle at the point marked 0 and open it up and straighten the circle until it is a flat line with the numbers running from 0 to 360.

There are two types of cycles with which Gann worked. The first are the time cycles, or natural cycles, and the second is directly related to the price movement of the stock, index or commodity being analyzed. To take the natural cycle of one year in weeks is to look at 13 weeks as one quarter (90 degrees), 26 weeks as one half (180 degrees), etcetera, so, that the cardinal points of this cycle, as viewed on a circle appear as shown. (Figure 5) Placing this cle on a geometric scuare, for use on the square charts, gives Tis the square of 52. jhigure 6).

Two cycles of this square is 104 weeKs or 720 degrees, and 208 weeks is four years or cycles. The ten year cycle is 520 weeks. Since ten years is a very important cycle in itself, we should view it also as a circle.

We can take a major cycle, such as the 30 year cycle, and view it as the following:

30 years or 360 months

22 1/2 years is 3/4 or 270 months

20 years us 2/3 or 240 months

15 years is 1/2 or 180 months

10 years is 1/3 or 120 months

7 1/2 years is 1/4 or 90 months

5 years is 1/6 or 60 months

3 3/4 years is 1/8 or 45 months

1 7/8 years is 1/16 or 22 1/2 months

1/12 is 30 months

1/32 is 11 1/4 months

So, these are the natural cycles, and the method that Gann used was to place these on a chart in a square form. The second set of squares which Gann used were those generated by the movement of price. By viewing the- high, low, and range of movement in the >rice in this same cyclical fashion, he invented the squares of the ligh, low, and range. So, on a circle, assuming a range in prioe of 60 points, the cyclical form of that movement would appear as shown in Figure 7.

.. Placed in a square, and applied to a weekly chart, the most important part of the cycle would be 60 weeks, or points. Thirty weeks, also being important, but secondary. Of course, a 30 point move would be a fifty percent retracement (180 degrees). The cycles which Gann used, both those from the cycle of the years and those from price, must indicate a change at regular intervals. The key word here is CH/VNGE, and if change is not evident, it is unlikely that the cycle is valid. The cycles do not necessarily run from low to low, showing a sine weve type of formation, but indicate a change. In other words, the one year cycle could run from low to high, with a reversal after one full year. It may, also, show price rising for 270 days, and then correcting for 90 days into a second low at one year from which price again rises.

In general, the best setup from the cycles is to have three or more coming out at the same time period on a chart. A typical setup would be longer term cycles, such as five year and seven years, with a shorter term cycle such as a 90 day cycle, in which price accelerates in that time frame into a blow off movement.

Returning to the circle, and its divisions. The angles which Gann used come from this source. In the remainder of this book you will find references to 1X1 angles or angles that travel at the rate of 1 point per time period, this is a 45 degree engle. This 45 degree angle could be 1 cent per time period. It is just the simple matter of traveling one unit of price per one unit of time. You will see the same references to 2X1 angles, and 4X1 angles, although the latter is used sparingly. These angles are all referred to on the basis of "rise over run", or the price level followed by the time period on the chart. A 1X2 angle, or an angle