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4 If you look at the Square of Nine chart, you will also see circles or rings, which have been drawn around certain squares. The last circle has calendar dates that revolve in a clockwise fashion around the square base, which starts from the date March 21 st. This is the vernal equinox, when the Sun is at 0° Aries, also known as the l" day of spring and represents the beginning of the natural year. Actually, the Sun does not move, it only appears to be at 0° Aries. In reality, the Earth, which revolves around the Sun, as one of its many satellites is at the opposite sign of 0° Libra. We will get into more detail of the Zodiac in a little while. The first inner most circle has a radius that runs from the center down to the cardinal number 352. This number appears on the same cycle or level of pyramid blocks as the number 360, which is 8 blocks to the left of 352. As you know, there are 360° in a circle and this is why Gann has a ring around this particular square. The next circle or ring from the center has a radius that runs down to the cardinal "+" number 716. This number appears on the same cycle or level as the number 720, which equals 2 times 360 and is the reason the 2" ring is located here. The third ring runs through the number 1080, which equals 3 times 360, etc. Gaim set his 3 ring radius 4 blocks below the 2" ring, which was the amount of space or blocks between ring 2 and ring I. The reason for constructing a chart like this is based upon the hypothesis that each positive whole number, i.e. the regular counting numbers!, 2, 3, 4, 5, etc. all correspond to some specific angle of a circle between 0° and 360°. Pythagoras, one of historys greatest mathematicians and philosophers said " Units in a circle or in a square are related to each other in terms of Space & Time at specific points." The Square of Nine is unique
in that it achieves the ancient practice of squaring the circle and is often called The Pythagorean Cube. Notice how the square completes at the comer number "X" 361 on one of the 45° angles ofthe Square of Nine, the 315° angle. Ifyou started with a zero in the center, it would have came out exactly at 360. Notice how the 2" ring firom the center has a radius that runs through 720, (2 x 360) as stated earlier, but also perfectly inscribes the 361 block (square base) within its radius. Now if you look at the number "4" on the chart and follow an angle of 45° going up to the top right hand comer, you get the number series: 4,16, 36, 64,100,144, etc. These numbers are all squares of even numbers, i.e. 2 x 2, 4 x4, 6 x 6, 8 x 8, 10 x 10,12 x J2, respectively, etc. If you look at the number "1" on the chart and follow an angle of 45° going down to the bottom left hand comer, you get the number series I, 9,25,49, 81, 121, 169, etc. These numbers are all squares of odd numbers, i.e. 1x1,3x3, 5x5, 7x7, 9 X 9,11 X 11, 13 X 13, respectively, etc. Garm said, "We use the square of odd and even numbers to get, not only the proof of market movements, but the cause". This particular arrangement of numbers on the Square of Nine creates a very unique square root relationship with all the other numbers on the Square of Nine chart. My friend, Michael S. Jenkins illustrates some interesting square root trading techniques utilizing the Fibonacci ratios with the Square of Nine in his Stock Trading Course and his book Chart Reading for Professional Traders.
Navigating with the Square of Nine Basically, if you want to move in cycles of 360° around the Garm Wheel you take the number you are interested in such as the all time High or Low price, take the squareroot of the number, then add or subtract 2 from the root and resquare the result. Example: Lets say that we are interested in Ihe price 664 (which is in the vertical column straight up from the center). The square root is 25.768 + 2 = 27.7682 = 771, which is the number directly above 664 or one ftill 360° degree cycle out firom center. If we subtracted 2 from the squareroot and resquared the number (25.7682 = 23.7682 = 564,9) we would get 565. which is directly below 664 or one fiiU 360° degree cycle in towards center. The reason this works is that the squares of the "even" and "odd" numbers line up on a straight line from the apex or main Center Square of the chart. Its also mathematically simple to observe that all odd numbers are separated by units of 2, such as I, 3, 5, 7, 9, 11, etc. The same is obviously true for all the even numbers: 2, 4, 6, 8, 10, 12, etc. This is why adding or subtracting "2" to the squareroot of a number, then resquaring the sum is equivalent to a 360° cycle on the Square of Nine. Another mathematical proof is that Vi a circle is 180° and we can see that the squares of the "even numbers" line up on the opposite side of the Square of Nine to the squares ofthe "odd numbers". We leamed that adding "2" to the square root of a number, resquared was equal to 360°. Therefore, adding "1" to the square root of a number, resquared would have to be equivalent to 180°, because Vi of 2 equals "1" and Yi of 360° equals 180°. If we wanted 90° relafionships, we would add or subtract 0.5 to the square root, then resquare because 90° is V* of 360 and of 180° and 0.5 is of "2" and Vz of "1", etc.
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