THE SQUARE OF NINE

The “Master Price and Time Calculator”, which is popularly known as the Square of Nine happens to be one of the most interesting discoveries by W. D. Gann. Square of Nine is pyramidal arrangement of numbers and possess great ability to forecast price and time cycles. This article is an attempt to summarise mathematical principles behind the Square of Nine.

Below is a snapshot of the Square of Nine:

133	134	135	136	137	138	139	140	141	142	143	144	145
132	91	92	93	94	95	96	97	98	99	100	101	146
131	90	57	58	59	60	61	62	63	64	65	102	147
130	89	56	31	32	33	34	35	36	37	66	103	148
129	88	55	30	13	14	15	16	17	38	67	104	149
128	87	54	29	12	3	4	5	18	39	68	105	150
127	86	53	28	11	2	1	6	19	40	69	106	151
126	85	52	27	10	9	8	7	20	41	70	107	152
125	84	51	26	25	24	23	22	21	42	71	108	153
124	83	50	49	48	47	46	45	44	43	72	109	154
123	82	81	80	79	78	77	76	75	74	73	110	155
122	121	120	119	118	117	116	115	114	113	112	111	156
169	168	167	166	165	164	163	162	161	160	159	158	157

• The Cardinal cross (highlighted in Grey) : 0º OR 360º / 90º / 180º / 270º

• The Diagonal cross; edges of the pyramid (highlighted in Blue) : 45º / 135º / 225º / 315º

• In it’s most intuitive form, the Square of Nine starts with number 1 in the centre of the square.

• It progresses from the number 2 in clockwise direction to complete first full rotation at the number 9, hence the name Square of Nine. Please note that 9 is a square of odd number 3.

• Every rotation thereafter ends with square of subsequent odd numbers on diagonal cross at 225º. e.g. second rotation ends with the number 25 (square of 5); third rotation ends with the number 49 (square of 7) and so on.

• All odd number squares minus one, divide evenly by 8. For example, (9 – 1 = 8), (25 – 1 = 24), (49 – 1 = 48), (81 – 1 = 80) are all exactly divisible by 8.

• Starting on the number 4 and moving upward to the top right corner, all the even number squares are aligned (highlighted in Green). These numbers are 4, 16, 36, 64, 100, 144 and so on. The number 4 is the square of 2. The next numbers are the squares of even numbers 4, 6, 8, 10, 12, and continue on.

• The odd (at 225º) and even (near 45º) number squares are opposite each other on the Square of Nine. Even number squares are placed just above the diagonal cross at 45º.

• All even number squares divide evenly by 4. For example, (4/4 = 1), (16/4 = 4), (36/4 = 9), (64/4 = 16), (100/4 = 25), (144/4 = 36). Interestingly, when an even number square is divided by four, the resulting number is always a square number. e.g. 16/4 = 4 (square of 2), 36/4 = 9 (square of 3), 64/4 = 16 (square of 4), 100/4 = 25 (square of 5), 144/4 = 36 (square of 6) and so on.

• The number 8 is of great significance in the working of the Square of Nine. Law of vibration calls the number 8 a MYSTIC; a number with magical properties. M vibrates 4, Y vibrates 7, S vibrates 1, T vibrates 2, I vibrates 9 and C vibrates 3. Hence vibration number of MYSTIC is 4 + 7 + 1 + 2 + 9 + 3 = 26 => 2 + 6 = 8.

• Calculations on the Square of Nine are not based solely on the position of odd and even number squares, but also on the number 8. Each rotation on the Square of Nine contains 8 more numbers than the previous rotation.
  
  Rotation 1 has 8 numbers from 2 to 9
  Rotation 2 has (8 + 8 = 16) numbers from 10 to 25
  Rotation 3 has (16 + 8 = 24) numbers from 26 to 49
  Rotation 4 has (24 + 8 = 32) numbers from 50 to 81
  Rotation 5 has (32 + 8 = 40) numbers from 82 to 121 and so on.

• The cardinal and diagonal axis altogether divides one full rotation from odd number square to the next odd number square in 8 equal parts. For example, a rotation starting from the odd number square 121 to the next odd number square 169 is divided into following 8 equal parts:
  
  169 – 121 = 48
  
  121 + (1/8 of 48) = 121 + 6 = 127 at 180º cardinal axis
  121 + (2/8 of 48) = 121 + 12 = 133 at 135º diagonal axis
  121 + (3/8 of 48) = 121 + 18 = 139 at 90º cardinal axis
  121 + (4/8 of 48) = 121 + 24 = 145 at 45º diagonal axis
  121 + (5/8 of 48) = 121 + 30 = 151 at 0º OR 360º cardinal axis
  121 + (6/8 of 48) = 121 + 36 = 157 at 315º diagonal axis
  121 + (7/8 of 48) = 121 + 42 = 163 at 270º cardinal axis
  121 + (8/8 of 48) = 121 + 48 = 169 at 225º diagonal axis
  
  in other words,
  
  the number 133 is 2/8 OR 1/4 i.e. one-quarter point
  the number 145 is 4/8 OR 1/2 i.e. the half-way point
  and the number 157 is 6/8 OR 3/4 i.e. three-quarter point
  in the rotation from 121 to 169 on the Square of Nine.

• W. D. Gann placed importance on the diagonal cross because the 225º angle mark the exact locations of the odd number squares, the 45º angle mark the approximate locations of the even number squares and the 135º and 315º angles mark the half way points between the odd and the even number squares on the Square of Nine.

• W. D. Gann placed importance on the cardinal cross because the 0º, 90º, 180º and 270º angles mark the exact locations of the quarter points between the odd and the even number squares on the Square of Nine.

• Other important angles on the Square of Nine are 60º, 120º, 144º, 216º, 240º and 300º.