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# Hexagon Chart

The Hexagon Chart is a tool of technical analysis which was first popularized by stock market forecaster W. D. Gann. The chart first appeared in his corespondence course Master Charts, which is now a part of the W. D. Gann Master Commodities Course. It is very similar to another tool used by Gann, the Square of Nine, another tool described in the Master Charts.

## Construction

The Square of Nine consists of the integers arranged in the form of a hexgonal spiral. One can construct it using a spreadsheet or graph paper. Place the number 0 in a central cell; to its lower left place the number 1; to the right of 1 is 2; and to the upper right of 2 is 3, and continues to go around the center square. When it gets to 6 to the left of zero, it completes the first layer of hexagon. The second layer starts by adding 7 to the lower left of 6, and so on. Below is an example going up to 60:

 ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ ¯¯ 56 55 54 53 52 57 33 32 31 30 51 58 34 16 15 14 29 50 59 35 17 5 4 13 28 49 60 36 18 6 0 3 12 27 48 37 19 7 1 2 11 26 47 38 20 8 9 10 25 46 39 21 22 23 24 45 40 41 42 43 44 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

Mathematically, the Hexagon Chart is a graphical representation of the centered hexagonal numbers. The sequence is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. However, it should be noted that the center of the Hexagon Chart starts with zero instead of one, so all numbers in the sequence are reduced by one.

### Spiral direction

In the original Hexagon Chart used by Gann, the direction of the numbers spin counterclockwise. Patrick Mikula explains that it is because, onto the Square of Nine, Gann liked to overlay astrological charts, most of which spin counterclockwise.

## Angular value of each number

### Zodiacal relationship in the Hexagon Chart

In Master Charts, Gann assigned the following method to overly the planetary positions on the chart:

• The axis going from 0 to 1,11, 28, and so on are 60° or 0° Gemini.
• The axis going from 0 to 2, 10, 24, and so on are 120° or 0° Leo.
• The axis going from 0 to 3, 12, 27, and so on are 180° or 0° Libra.
• The axis going from 0 to 4, 14, 30, and so on are 240° or 0° Sagittarius.
• The axis going from 0 to 5, 10, 24, and so on are 300° or 0° Aquarius.
• The axis going from 0 to 6, 10, 24, and so on are 0° or 0° Aries.

In most astrological charts, 0° Aries is represented by the horizontal axis pointing to the left. Therefore, the sequence 6, 18, 36 goes left horizontally from the center accordingly.

### Mathematical formula

For any natural number P>1, its approximate angular value A (in degrees) is given by:

Ap = MOD[210×P½−180,360]°

For example, from the Hexagon Chart, it is known that the angular value of 36 is 0°. Substitute P with 36 into the above formula:

A36 = MOD[210×36½−180,360]° = 0°

In Microsoft Excel, if the value of P is input into the cell A1, then the formula to calculate the angle is MOD(SQRT(A1)*210-180,360). In OpenOffice Calc, the same formula could be used except that the comma has to be replaced by a colon. Below are some examples using the formula in Excel:

A B (The fomula in the cell in B)
1 10 124.0783086 <--MOD(SQRT(A1)*210-180,360)
2 20 39.14855055 <--MOD(SQRT(A2)*210-180,360)
3 30 250.2173708 <--MOD(SQRT(A3)*210-180,360)

Conversely, if a trader is given a certain angle, and he wants to know what numbers are sitting on that angle, he can also compute it in Excel. Suppose the value of A is input into the cell B1, and the number of revolution is input into A2, then the formula is ((B1+360*A2+180)/210)^2. Below are some examples:

A B (The formula in the cell in B)
1 Rev. \ Angle 270
2 0 4.59183673 <--((B1+360*A2+180)/210)^2
2 1 14.8775510 <--((B1+360*A3+180)/210)^2
4 2 31.0408163 <--((B1+360*A4+180)/210)^2
5 3 53.0816327 <--((B1+360*A5+180)/210)^2
6 4 81.0000000 <--((B1+360*A6+180)/210)^2

### Angular locations of perfect squares

In the Hexagon Chart, the perfect squares are always 210° apart, for example:

• The number 1, or 1×1, is at 30°.
• The number 4, or 2×2, is at 240°, which is 210° after the angular location of 1.
• The number 9, or 3×3, is at 90°, which is 210° after the angular location of 4 (after deducting one circle of 360°).
• The number 16, or 4×4, is at 300°, which is 210° after the angular location of 9.
• The number 25, or 5×5, is at 150°, which is 210° after the angular location of 16 (after deducting one circle of 360°).

In contrast, the perfect squares in the Square of Nine are always separated by 180°, making them diagonally opposite.

## Practical examples

Patrick Mikula stated that the most important angles in the Hexagon Chart (or aspects as they are called astrologically) are the multiples of 60° and 90°, i.e. 0°, 60°, 90°, 120°, 180°, 240°, 270° and 300°. The differences of these angles, like 30° and 150°, are also important. If the current price makes these aspects with some important support or resistance level, then the price is likely to turn. Here are a few actual trading examples in Corn given by Gann in How to Make Profits Trading in Commodities: A Study of the Commodity Market.

Date Corn Market Planetary Aspects Price-Planet Aspects ¢ Off % Off
Oct 1866 Bottom at ¢33¾. Venus (312°) square Saturn (222°) ¢33½ (311°) conjunct Venus and square Saturn. ½ 1.5%
Oct 1884 Bottom at ¢34½ Venus (173°) square Saturn (83°) ¢34 (324°) inconjunct Venus and trine Saturn. ½ 1.4%
Jun 1891 Top at ¢75½ Venus (72°) square Saturn (162°) ¢75¾ (208°) seiquisquare Venus and semisquare Saturn. ¼ 0.3%
May 1916 Bottom at ¢63 Venus conjunct Saturn (104°) ¢62¾ (44°) sexile the conjunction. ¼ 0.4%
May 1920 Top at ¢197 Venus (34°) trine Saturn (154°) ¢192½ (214°) opposite Venus and sexile Saturn. 2.3%
May 1923 Top at ¢84½ Venus (73°) trine Saturn (193°) ¢84¾ (313°) trine both Venus and Saturn. ¼ 0.3%
Mar 1925 Top at ¢137 Venus (224°) trine Saturn (344°) ¢135½ (104°) trine both Venus and Saturn. 1.1%
Jun 1928 Top at ¢122 Venus (75°) opposite Saturn (255°) ¢122½ (344°) square both Venus and Saturn. ½ 0.4%
Jul 1928 Bottom at ¢76½ Venus (133°) trine Saturn (253°) ¢77 (223°) square Venus and sexile Saturn. ½ 0.7%
Jun 1930 Top at ¢88 Venus (100°) opposite Saturn (280°) ¢87¼ (342°) trine Venus and sexile Saturn. ¾ 0.9%
Apr 1931 Bottom at ¢51½ Venus (353°) sexile Saturn (293°) ¢50½ (233°) trine Venus and sexile Saturn. 1 1.9%
Apr 1932 Bottom at ¢27½ Venus (63°) trine Saturn (303°) ¢26¾ (186°) trine both Venus and Saturn. ¾ 2.7%
Oct 1933 Bottom at ¢44 Venus (250°) sexile Saturn (310°) ¢43¾ (129°) trine Venus and opposite Saturn. ¼ 0.6%
Apr 1934 Bottom at ¢40 Venus conjunct Saturn (324°) ¢41 (84°) trine both Venus and Saturn. 1 2.5%

Please note that the minimum fluctuation in corn futures is ¼ cent. Also, the price-degree conversions are based on the formula described in the previous section, instead of the exact graphical angles on the Hexagon Chart.