To locate our current position in any trade, at any time, we go to the “Pythagorean Cube”.
Gann referred to this calculator as his “Square of Nine”. We have referred it to you as being basic to most references and patterns in the universe.
Again, it preceded Pythagoras considerably, since its calculations are found in the Great Pyramid (some 2500 years B.C.) and its use included that of being a calendar as well as a square root calculator for the early Egyptians, as stated earlier.
Following is a version of this calculator and a “table version” which we hope may throw some light of reference to the spiral chart. This will be our “Bell Cow” for reference as we teach onward.
Please note that all squares in the PYRAPOINT technique are calculated per height (PRICE) and per length (TIME). Since all calculations are based upon the determinations of the square root calculator (to which you are soon to be introduced) our next step should be to learn the basics of this calculator.
Note: The following example of the “P.C.” is the type used by Gann in his seminars. The second chart is a table to give a “flat” dimension to the Square of Nine (“P.C.”).
Of special note on this calculator is that the square root before mentioned is evident on the 135-degree and the 315-degree lines. From the center of the calculator at “1”, follow the line outward down the 315 degree line and you will note that each cycle is represented by a number which is the square of an odd number. The first cycle, 9, is the square of odd number 3. The second cycle, 25, is the square of the odd number 5. The third cycle, 49, yields square of the odd number 7, etc.
By the same analogy, from square 1, note that travel upward along the 135 degree line finds the squares of even numbers -- each just prior to the 135 degree dissection line. Squares represented here -- 4, 16, 36, 64, etc. -- are all squares of consecutive even numbers.
This brings us to an interesting (and vital) point in our analogy. If you were to begin at an odd number, say 121 (square of 11 or “11th square”), and you desired to follow the numbers upward to the square of the next number, 12, you would be located 180 degrees across from where you began -- halfway around the calculator. Obviously this puts you on the 135-degree line, stopping at number 144 or “12th square”. You began 180 degrees away on the 315-degree line.
Past number 144, you are obviously traveling into the 13th square, which will finish on the next square beyond your number 121 starting point -- or 169 (which is the square of 13).
At this point, the author feels that you have discovered one of the big errors followed by most Pythagorean Club scholars. This is the fact that you have traveled a complete circle, or cycle, as some scholars address it. However, you have
not one square, as is so often shown, but two! You have completed square of 11, and also the square of 12 within this cycle. Thus it follows that since there are eight 45-degree segments in the complete cycle, there should be four 45-degree segments in half of the cycle -- or one square. And so it is -- 180 degrees from the beginning of the cycle to the end of the square (45 x 4 = 180).
Now it must by evident to you that square root determines the square in which you are trading, and the 45-degree lines provide the parameters of resistance in your trade. Square root also determines the next square in your price parameters. If price is 121, you know this is the 11th square on the Pythagorean Cube. Your own hand calculator tells you this -- and it will tell you that this square proceeds until 144 where your hand calculator says this is the square of 12. What may not be so obvious is the fact that we could stop at the halfway point and we could determine that number as well. Let’s try it.
One-half way from the 315 line to the 135 line would put us at the 45-degree line. Following this line to its square yields a price on that 45-degree line on the “P.C.” of 133. Therefore, since 133 is square of 11.5, we are definitely on target.
Following this analogy, we should be able to identify one-fourth of this square of numbers (be it PRICE or TIME). Thus if 11.5, squared, equaled one-half way between square 11 and square 12, then 11.25 squared, should give the one-fourth point. Thus the one-fourth point should reflect one-fourth of the full 180 degrees (or 45 degrees from the beginning) between squares 11 and 12. So let’s check 11.25, squared, and we find it 45 degrees from our point of beginning or nearly on top of the 127 line of dissection.
This shows us a very important fact: .25 added to the square root of a number on the “P.C.”, the sum then squared, will yield a number 45 degrees up on the “P.C.” calculator. This is true for any number. It is also true if you subtract .25 in a down series, or market. IT IS UNIVERSAL!
Now we have a means of answering the question (for any number representing a top or bottom) as to how far we are from the next 45 degrees, 90 degrees, etc. of resistance in this wave, which we may be trading. We can also take the square root of this same number and convert it to time as long as we use Pythagorean scales and PYRAPOINT rules.