Sometime during the late 1930's, or early 1940's, W.D. Gann generated a "spiral chart" that was clearly based on the quadratic function y=aX^2+bX+c.  Eventhough his Master Stock Course (1st edition in 1937 to 5th edition in 1953) shows a  graphic for and discusses both a "square of nine" and this "spiral chart" as two completely different entities, somehow the spiral chart has come to be referred to as the "infamous" SQUARE of NINE and/or the NATURAL SQUARES CALCULATOR.

While the graphic below is not the actual "Spiral Chart" identified by Mr. Gann in his Master Trading Course, it follows the same rules and is a LOT CLEARER to see for discussion purposes. If you want to view the actual Spiral Chart and Square of Nine then go page 402 in the Master Stock Course.


While Mr. Gann "DID NOT" identify this SPIRAL TABLE as the infamous "SQUARE OF NINE (9), or the Natural Squares Calculator, those are "now" the common names given to this method by the world trading community.

While I'm not sure how many large speculators are using it to actually trade with, not that many I suspect, I am very sure that there not many who understand it's "true purpose":  of "locating" points on a parabolic curve that a stock, or stock index, MAY BE attempting to form "over the intermediate term to long term trend periods"...more than a few months.  

OF course, many people do not understand the dirty details or basis for a lot of tools and methods they use, and neither is that a necessity.  However, in this case, where the underlying basis of the tool AND it's actual performance is "highly questionable," some of those people may want to dig a little deeper into the nuts and bolts of it. 

The simplified version of this function, or formula, becomes just y=X^2 if we only use one factor of X and block the other two at zero. In other words, y=X^2+0X+0 becomes simply y=X^2.   However, let me also point out to those with a firm footing in mathematics, that I fully realize that by dropping the 2nd and 3rd terms that the parabola can not be "positioned" mathematically, but for this discussion, and the real world application to stock trading that is irrelevant.

AS for the the SPIRAL chart itself, or SQ-9 if you prefer, both are nothing more than a simple "short cut" or "look up table" for finding parabolic curves that have different "rates" of progression....as in ROC or rate of change.  That is to say,  those with "different," but periodic, values for the X time variable when "plotting"  these curves on a screen...or drawing them by hand on graphing paper.

In simpler terms, the underlying key to understanding this "calculator" is that: the Y values for all "possible" parabolic curves remains the same ,  and it is only the values for each curves "time period,"  or X, and the time to "step" between those Y value "points" on the curve THAT CHANGE.  Hum!  

Those Y points along ALL "potential" parabolic curves for a stock or commodity trend are located at numbers referred to as the "natural squares." For Mr. Gann's work, or at least for that SQ-9 calculator, which does not accept fractions, these numbers are:  "2" as in 1x1=2, "4" as in 2x2=4, "3" as in 3^2=9, "4" as in 4^2=16, and then 25, 36, 49, 64, 81, 100, 121, 144 (12^2) and SO ON out to where ever or infinity.  

Once again, it's only the time "periods" for X that changes.  In this manner, a stock, or any moving and advancing data series (from the price of eggs, wheat, or gasoline, to bond prices) that moves from 9 to 16 in 1 year will have a higher rate of change and "angle" to it's parabolic curve than a stock, or other data, that moves from 9 to 16 in two years, and it would be advancing or "accelerating" at a lot "steeper angle than a stock that advanced from 9 to 16 in say 5 years.  

GET IT NOW?  No!  Well, I''ll bet some long time Guru's just popped the proverbial light bulb.  As for the rest of you, just hang in there and well get you home, eventually, and if not sooner rather than later then you can always "pop" for $19 and then call us...where well play "designated driver" and get you home for sure.   

Of course, only one move between any "natural square points," on our graph, like 1 to 4, or 4 to 9, or 9 to 16, or 16 to 25--and so on--DOES NOT make a "trend" either.  That is to say, only one "mark" along a potential parabolic curve DOES NOT confirm is "rate of change," and by default, this single "mark" does not confirm it's PERIODIC VALUE for "X" in time. 

However, if a stock should go on and "touch" a progression of these "natural square points" AND IN "approximately even" time steps for X, THEN we would have the makings of a Parabolic Curve, a quadratic model, and the basis for a "real" formula to predict that "one curve" we located by "estimation" and observation."  OF course, that "estimation" would only be valid for as longs trend remains on track and following that same, "periodic," time for X.  GET IT NOW?  Say what!

I know this may be somewhat confusing for those without a solid background in math and science, eventhough, this is actually not complex math, and this next little graphic should help some.   IF NOT, you best "subscribe to our service" and then give us a call.

<Graph: Parabolic Curves--different time steps for different rate curves>  

Anyway, for the graphic BELOW, if you look over the upper part of the graphic and read the comments that go with it, you can see why Mr. Gann, or who ever, no doubt THOUGHT this parabolic curve was the most likely "natural curve" for stock prices to follow, over AT LEAST the intermediate to longer term...if they follow any!   

<KEY COMPARISONS between Parabolic and Exponential Growth.>

UNFORTUNATELY, after having another 50 years of data to "fit" a curve to, and then actually "thinking about" WHY stock prices would have a strong tendency to follow it, and not other curves, we now get a clearer picture. This more up to date and modern day picture supports OUR assertion that Mr. Gann, or who ever developed this method, WAS WRONG about parabolic curves, and the real "natural geometric curve" that stocks ACTUALLY tend to follow is the EXPONENTIAL GROWTH CURVE.

In addition to the excellent visual confirmation of this by many, many, long term and intermediate term stock and index charts, we have the undeniable fact that STOCKS "absolutely" should form exponential curves.  That is  BECAUSE their underlying mathematical basis is the compounding of interest, and/or "retain earnings."  Needless to say, we also note that the standard formulas used to calculate "compounding" do produce pure exponential growth curves...AND ALSO "exact" Fibonacci curves too (which is another story entirely).

That crude curve example we placed on the graphic, and the table to go with it, gives you a good 'basic idea" of where we are coming from, and a good starting point for your own analysis...if you want to dig deeper into this underlying basis and fundamental concept for parabolic curves on your own.

By the way, for those with a GRAPHING CALCULATOR or a spreadsheet programs, and know how to use them of course, if you download the daily or weekly stock data for just about any big cap technology stock--with that data going back into the 1980's or 1970's--and cut off that data at their 2000 tops for a "best regression" fit from the beginning to that 2000 top, you will find that the R2 "correlation" is almost always better for the "exponential regression" (ExpReg) fit, than for a 2nd degree polynomial (QuadReg) fit.  

Oh, and needless to say!  A "LINEAR REGRESSION" of nearly any long term stock chart (a decade to many decades) or an intermediate term chart (a few years minimum to a decade) shows why the "linear regression" TECHNICAL INDICATORS on most trading software are nearly worthless for a trend once it has extend out for many months to a year or more.

 NOW, while I'm not going into it much more here, you can see that IF parabolic curves ARE NOT the natural curves that stocks "tend to follow," THEN that means that the SQUARE OF NINE, or Natural Squares Calculator, are "nearly" BOGUS.

WHY do I say "nearly bogus" you ask?  Because, it "appears that there are still enough traders "working" this bogus method that it "could have," and in some cases we see where it has had, "some influence" on the actual highs and lows...REGARDLESS of whether it's based on a fallacy or not.

That is to say, and in the simplest of terms, if enough people become convinced of a fallacy and support it with their money then the fallacy has become a self full filling prophecy and a new reality...at least for awhile and some of the time. 

 THAT IS why, WE DO spot the price, or index value, targets from this method on our Gann chart analysis, eventhough, we place little faith in them unless they stand in a "cluster" with targets from other, and more reliable, methods...like the Fibonacci retracements and key Market Cycle times.