## THE GANN WHEEL IS A SQUARE ROOT CALCULATOR

The Gann Wheel, what most people think of as the Square of Nine, is sometimes called a "Square Root Calculator" or a device that "Squares the Circle." This simple illustration may explain how and why these terms came about. You probably recognize that the illustration is just the first few rings of a Gann Wheel with the numeral "1" at the center.

31 | 32 | 33 | 34 | 35 | 36 | 37 |

30 | 13 | 14 | 15 | 16 | 17 | 38 |

29 | 12 | 13 | 4 | 5 | 18 | 39 |

28 | 11 | 2 | 1 | 6 | 19 | 40 |

27 | 10 | 9 | 8 | 7 | 20 | 41 |

26 | 25 | 24 | 23 | 22 | 21 | 42 |

49 | 48 | 47 | 46 | 45 | 44 | 43 |

In Square of Nine parlance we say things like

*19 is 90 degrees from 15.*That makes sense only if you can visualize that this rectangular table of numbers is enclosed in a circle (or series of circles) of 360 degrees. In this case, the number 19 is 1/4 the way around the circle from the number 15, or 90 degrees in circumference from 15. The number 34 is directly above the number 15 and positioned one circumference or ring outside the circle that contains the number 15. In the same sense that we can say that 19 is 90 degrees from 15, we can say that 34 is 360 degrees from 15, or one complete rotation of the circle from 15. So, that explains where squaring the circle comes from. A more accurate expression would be that we're circling the square but that never did catch on.

## HOW TO ROTATE AROUND THE GANN WHEEL

Here's where it gets fun. The square root of 15 is 3.87. Add two to the square root of 15 and we get 5.87. Square 5.87 and we get 34.49 which rounds to 34. Now we know that adding two to the square root of a number and squaring that sum is the same thing as a 360 degree rotation up on the Gann Wheel. If "2" represents a 360 degree rotation then "1" represents a 180 degree rotation, "0.5" a 90 degree rotation, and so on. W.D. Gann tells us that 90 degrees in very important in the stock market. What he's really saying is that adding and subtracting .5 (and exact multiples or proportions of .5) to the square root of a stock price and then squaring the result is very important! We acknowledge that there is is another school of Gann thought that will say that Gann's reference to 90 degrees relates to the movement of celestial bodies. We've looked into that and they may be right, but for our purposes we've also learned that these schools of thought can peacefully exist alongside each other without contradiction. A very few people have been using some variation of the Gann Wheel for about 100 years now. In his famous interview given to Richard D. Wyckoff in 1909, W.D. Gann attributed market movements to some undefined "law of vibration." People can disagree about what W.D. Gann meant by that but we, at least, are fairly certain he was talking about the principles underlying the Square of Nine.## WHAT IS SO SPECIAL ABOUT THE SQUARE OF NINE ?

The Square of Nine is unique because unlike every other method of tecnhical analysis, the Square of Nine is totally indifferent to whether the input variable is a price, a range of prices, or a number of trading days or calendar days. They are all the same and completely interchangeable. Say what? That can be a little hard to get your brain around after spending years studying chart patterns, exotic moving averages, and oscillators. That's the beauty of it. Price and time become interchangeable by converting them to degrees of a circle. Squares and square roots are part of that process. Once price and time are conceptualized only as degrees of concentric circles we could care less about their actual magnitude. At that point we care only about their orbital relationship. Are they in opposition, conjunction or square? You will find that almost every significant high or low pivot point is indeed in opposition, conjunction or square to a previous price, range or time. You can see a recent example of price-to-price relationships in our Square Root Theory article. Other possible relationships are price-to-time, range-to-price, time-to-range, and so on.Is this what W.D. Gann meant in that Wyckoff interview when he said

*"just as the pendulum returns again in its swing, just as the moon returns in its orbit, just as the advancing year over brings the rose of spring, so do the properties of the elements periodically recur as the weight of the atoms rises."*One other very special aspect of the Square of Nine is that the more you study the more you learn how much you don't know!

## ROADMAP CHARTS USE SQUARE OF NINE PRINCIPLES

Roadmap Charts are a simple and elegant construct that use square roots to convert price and time into channels and a mathematically precise grid that can contain a trend for days, weeks, months or even years. Although the channels look like conventional trend lines consider that trend lines are drawn after-the-fact to delineate existing data points.__Roadmap channels are fixed and can be drawn immediately__, within seconds in the case of intraday data, after the completion of a single price bar. That this phenomenon occurs more often than not is fairly convincing evidence that even such complex events as hugely participated auctions may be explainable by a few simple rules.

We often say that Roadmap Charts self-define the trend because if the selected bar is indeed a trend-changing pivot point the channels will contain all (or nearly all) future price movement in that time frame for the life of the trend. Roadmap Charts can be constructed for any ticker in any time frame. The principles of construction remain the same although the quirkiness of certain pricing data, such as low-price stocks, decimal currencies, and bonds in 32nds, can present some scaling challenges. Our book Trading the Square of Nine with a Pencil and a Calculator goes well beyond Roadmap Charts and tells you how to easily convert price and time into degrees of a circle, and the five different ways to square price and time for any ticker in any time frame. Review the Roadmap Charts. You have enough information to understand what we mean by "45 degree grid" because all our S&P charts are drawn in multiples or proportions of 90 degrees. You can use other grid sizes as in this example but we believe that consistency pays off once you become comfortable with the natural rhythm of a particular ticker. A perfect complement to the Square of Nine techniques we describe in our book is the displaced moving average technique for projecting price and time that we tell you about in our book J.M. Hurst Cycle Trading Without the Rocket Math.

source : http://www.tradingfives.com

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