Square of Nine

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Square of Nine Calculator

The Square of Nine calculator calculates a square of nine table to the necessary size, populates the table with data for the selected symbol and then facilitates analysis using the rotatable Gann Square Emblem and crosses.

The Square of Nine calculator floats in the work page with its Display Controls in the function bar at the top:



Square of Nine Table

The Square of Nine table, which has also been referred to as the Odds and Evens Chart or Pythagorean Square, is essentially a square root calculator.

sitm_squr9_tableconstructn.gifIt is constructed by listing an ascending sequence of numbers beginning at 1 in the center of the table, then 2 to its right, 3 above 2, and continuing along the outside of the square in a clockwise direction until the set amount of numbers have been added to the table.

After the first complete rotation, the square will have 9 in its lower left corner, after the second rotation 25 will be in the lower left corner.

As the table grows, numbers being the squares of whole odd numbers (1,3,5, 7, etc.) will proceed in 45 degree diagonal line down and to the left of the center (1) beginning with 9, 25, 49, 81 and so forth. Numbers being the square root of whole even numbers (2,4, 6, 8, etc.) will proceed in the opposite direction beginning with 4, 16, 25, 36, 64, 100, and so forth.

Numbers being the squares of half numbers, e.g. 2.5, 3.5, 4.5, etc. will populate the other two "corners" of the square, "even" half numbers (e.g. 2.5, 4.5, 6.5, etc) proceeding downwards to the right at 45 degrees, "odd" half numbers proceeding upwards to the left.

The numbers running horizontally and vertically from the center have a squares of quarter numbers, e.g. 2.25, 2.75, 3.25, 3.75, etc.


Cardinal Cross

The numbers in the main cross running vertically and horizontally, and intersecting at the number 1 in the center, are known as the Cardinal Cross. As mentioned above, each number on this cross will have a square root of "quarter numbers".


Ordinal Cross

The Ordinal Cross consists of the two 45 degree diagonal lines that intersect a the number 1 in the center.

The lower left line consists of numbers whose square root is an odd whole number.

The upper right line is bordered to its top by a parallel line of numbers beginning with 4 whose square root is an even whole number.

The upper left and lower right diagonal lines contain sequences of numbers whose square root is half way between whole numbers: 1.5, 2.5, 3.5, 4.5, etc.

Odd/Even Groupings

The diagonal line with numbers whose square roots are whole numbers is the dividing line between the group of numbers whose square root is even (located below and to the right of the diagonal line) and that group of numbers whose square roots are odd, found on the left and above the diagonal line.

Gann Emblem

The Gann Emblem consists of a square and an equilateral triangle, all of whose corners intersect with a circle.

The square and the triangle are aligned so that one corner of each initially is placed at the zero degree position.


In the software, the square emblem can be rotated by holding down the right mouse button and dragging the mouse to spin the emblem.

The Cardinal and Ordinal Crosses will also rotate at the same time.

Seasonal Time Circle

The "circle" part of the Square of Nine divides the year into Solar Degrees, and contains days of the year, with the eight Key Seasonal Times (dates) highlighted.


The square root table in the calculator is always constructed in a clockwise manner. When using the calculator to analyze a market trending upward, the Bull setting is selected in the Circle Direction Control command.

The dates on the Seasonal Time Circle will turn green and be arranged in a clockwise direction.


When the Bear setting is selected, the dates are listed in a counter-clockwise direction and the circle is colored red:


This change in direction allows the downward market to be correctly analyzed.

Key Seasonal Times

The Key Seasonal Times of March 21, May 6, June 22, August 8, September 24, November 8, December 22 and February 4 have roughly 45 degrees of separation from each other, a making a yearly cycle of 360 degrees, or approximately 365 days.

Two of the days correspond with the Solstices (June 22 and December 22) and two correspond to the Equinoxes (March 21 and September 24).

Using the Display Controls

Users can change the display of the Calculator using the Display Control commands in the function bar.

After the appropriate settings for display and size have been made, the emblem and crosses can be spun to check for alignments of time and price.


Data Display Controls

The data displayed in the Square of Nine Table represents the price levels at which swing reversals occurred on the swing chart for the symbol being analyzed.

The range and display of the price data is set in the Square of 9 Calculator Settings dialog box:


The first settings determine which Points groups will display, if any.

The next two settings determine how the swing calculations are performed. The color selectors on the right control the display of the swing data turning points on the Table.


Three levels of display are available.

Check the box of the groups that are to be displayed.



Compression refers to the minimum length of time on which the swing calculations are made. Periods, see next item, can further extend this.

For example, data from 3-day swing charts can be used to populate the Table. This will require a Compression setting of Daily and a Periods setting of 3.

The greater the level of compression, the more data will be required to be downloaded for the current symbol in order to conduct a worthwhile Square of Nine analysis.


This setting is central to the swing chart calculation.

A setting of 1 will look for a reversal in price based on the data for one previous compression setting. A Weekly compression with one (1) period will look to the previous week to determine whether a price reversal has occurred. A Weekly setting with three (3) periods will look to the previous three weeks for a point to calculate the swing.

The higher the setting, the less swings will be detected and displayed.

Note - If the Table does not have enough data to perform a worthwhile Square of Nine analysis, check how much local price data is available for the symbol. Open a price chart for the symbol and select Monthly intervals. If there is insufficient data to properly populate the Square of Nine Table, perform a Custom Data Download for the chart and then restart the Square of Nine calculator.

High/Low Color

For each points group that has its display check box checked, its display in the Square of Nine table can be controlled using the color selectors.

High refers to the price at which a swing from up-trend to down-trend occurred.

Low refers to the price at which a swing from down-trend to up-trend occurred.

Square Dimension Control

In order to effectively view the Square of Nine Table the Dimension, Zoom and Decimal controls must be used in a coordinated manner.

The dimension of the Square of Nine Table is important in order to effectively display the range of data to be analyzed.

In order to view all possible data, the size of the table should be set to slightly more than the highest price recorded for the symbol.

For example, IBM's highest price was $139.19 on 13 July 1999. In order to see all possible swings, the Square should be set slightly higher than the highest high. For IBM the Square Dimension Control should be set to around 145 or 150. If the dimension is set to 169 (a square number: 13 x 13) the table will be square with its corners touching the circle.

Note - The start price will always be 1. It is not possible to create a "customized" Square of Nine for a particular market or security.

Obviously, for some securities or markets the table will begin to extend beyond the visible margins of the work page. When this occurs, use the Font Size control to reduce the size of the calculator so that it is entirely visible on the work page, see next item.

This will also occur when the Decimal display is increased, see discussion below.

Square Zoom Control

The Font Size control is used to effectively zoom out in when viewing the Square of Nine Calculator.

Zoom Out

As the minimum dimension of the Square of Nine Table is determined by the highest high of the market or security, for some symbols (for example an index such as Dow Jones) a very large table will be required.

In order to view the data squares and interpret them using full Square of Nine functionality, the size of the display will have to be reduced so that the entire tool can be viewed on the work page.

This is accomplished by reducing the font size of the data displayed in the table. As the font size becomes smaller, the table will shrink and more of it will become visible within the margins of the work page.

The Font Sizes range from 1 to 15.

Zoom In

When dealing with very large Square of Nine Tables, the analysis can be undertaken while viewing the entire calculator.

After rotating the emblem and identifying potential turning points, then use the Font Size control to zoom-in and view the actual price level of the data point.

If after expanding the size of the table the point to be viewed has gone beyond the margins of the work page, hold down the left mouse button and drag the table across the work page until the point to be viewed is visible, see below.

Note - Once a change has been made to the Font Size, the mouse wheel (if available) can be rolled to increase or decrease the size.

Circle Direction Control

The Square of Nine Table is always constructed in a clockwise direction, see above. The data that populates the table will then be analyzed using the rotating emblem and Seasonal Time Circle on the outside of the calculator.

While the data table remains static and the symbol's data remains in the same position, the direction of the Seasonal Dates on the Time Circle will change depending on whether the market or price formation being analyzed is Bullish or Bearish.

Bull Market


When the market or price formation is trending upwards, select Bull and the Seasonal Dates on the Time Circle will be displayed in a clockwise sequence and the circle will be colored green.

Bear Market

When the market or price formation is trending downwards, select Bear and the Seasonal Dates on the Time Circle will be displayed in an anti-clockwise sequence and the circle will be colored red.

The correct alignment of time and price can now be made.

Decimal Size/Position Controls

The third important component in displaying the data results is the Adjust Decimal size setting.

In order to properly display the required number of decimal places, the Dimension and Font Size controls must be used in conjunction with the Adjust Decimal command.

In the following example, we will analyze the top swing of Starbucks Corporation (SBUX on NASD). Its top occurred on 30 November, 2006 at $40.01.

The default decimal setting is zero (0).

In the first example below, the Square of Nine Table's Dimensions are set to 49, slightly above the highest swing top so that it is included in the display when the Calculator is open, the default decimal setting (0) is applied:



Dimension: 49 boxes

Dimension: 500 boxes

Font Size: 15

Font Size: 8

Decimal Places: 0

Decimal Places: 1

In the first example the value of 40 is included in the table, but SBUX is quoted in dollars and cents.

To view the cents, increase the Decimal setting. In order to continue viewing our target of $40.01 the Dimension of the table must also be increased, and in order to continue viewing the calculator on the work page the Font Size must be decreased. The above example on the right shows the result on a larger table of the one (1) Decimal place setting.

However, for a more thorough analysis, two (2) decimal places are required as SBUX is quoted at two decimal places.

Again the Dimension must be increased, and the Font Size decreased further.

On the following example the Dimension is 5000, the Font Size is 3 and two decimal places are displayed:



Dimension: 5000 boxes

Dimension: 5000 boxes

Font Size: 3

Font Size: 8

Decimal Places: 2

Decimal Places: 2

At this point the numbers become hard to read.

Use the Font Size to Zoom In (increase the Font Size) and use the left mouse drag function (see below) to keep the 4001 square visible in the work page.

Now the target value can be easily seen and it corresponds to $40.01.

Zoom Out to adjust the rotating Square of Nine Emblem to analyze the values, and then Zoom In again to check the time and price values.


As with most work pages in Your SOFTWARE, the News headline display will appear in the far right section of the function bar.

Each time you open a new screen, or refresh the data, the most recent news headline will be retrieved and displayed.

Single left-mouse click on the Headline to view it in the News Article window of the News work page.

The work page also includes a list of other Breaking News and a Search News facility containing search and news filter tools.

For more information, go to the Headline News help topic.

Positioning the Square of Nine Calculator


When large dimensioned tables are used they will often expand beyond the boundaries of the work page unless the Font Size is reduced.

In order to read the table's data, increase the Font Size and then drag the data back on to the work page using the mouse.

Hold down the left mouse button (the primary button) and drag the calculator around on the work space until the required part of the calculator is visible.

Locating the spot in the table to be viewed may take a series of zooms in and out. If available, the mouse wheel can be used to zoom in and out once a Font Size change has been initiated.

The combination of zooming in and out and dragging the display into the visible section of the work page can quickly display any point on the calculator.

Dynamically Aligning Time and Price

The Gann Emblem in the calculator rotates while the Square of Nine Table and the Seasonal Time Circle remain fixed. This allowing the time represented by the Key Seasonal Dates to be aligned with the price data that is displayed in the Square of Nine Table.


To rotate the emblem, hold down the right mouse-button (the secondary button) and drag the corner of the emblem to the spot on the Seasonal Time Circle that you want to analyze or compare.

The Square, Triangle and both Ordinal and Cardinal Crosses rotate together.

The order of the Seasonal Time Circle is clockwise when analyzing an upwardly trending price movement, and counter-clockwise for downward price formations. The direction is changed using the Circle Direction command in the calculator's function bar, see above.

Each can be rotated and aligned with various times to determine their relationship with the symbol's swing chart turning prices.

Using the Square of Nine Calculator to forecast and confirm alignments of time and price is a powerful but complex exercise. While the Square of Nine Calculator is a vast improvement on manual overlays of printed tables and charts, much study is still required to master the technique.

Comprehensive training in the Square of Nine Calculator's use and interpretation is available in David Bowden's Master Forecasting Course.

Refer to the Safety in the Market website for more information: www.safetyinthemarket.com.au

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