The square wheel
The classic Square of 9: numbers spiral out from 1, eight spokes to a turn. Enter a price for its levels every 45°, or a whole number to see which ring and angle it sits on.
Above 68,124.00
- +45°68,254.57
- +90°cross68,385.26
- +135°68,516.07
- +180°cross68,647.01
- +225°68,778.08
- +270°cross68,909.27
- +315°69,040.58
- +360°full turn69,172.02
Below 68,124.00
- −45°67,993.56
- −90°cross67,863.24
- −135°67,733.05
- −180°cross67,602.99
- −225°67,473.05
- −270°cross67,343.23
- −315°67,213.54
- −360°full turn67,083.98
68,124 sits on ring 131, 315.66° clockwise from east.
Cardinal cross and diagonals
Four of the eight spokes form the cardinal cross: 90°, 180°, 270° and the full turn at 360°. The other four are the diagonals at 45°, 135°, 225° and 315°. In the table the cross is in gold and the diagonals in blue.
Each 45° step adds 0.25 to the square root. From 68,124, whose root is about 261.006, the first level up is (261.256)², about 68,254.6, and the 90° level is about 68,385.3.
Where a number sits
On the spiral, 1 is the centre, 2 to 9 make the first ring, 10 to 25 the second, and each ring adds eight more cells. Angles here run clockwise from east, the direction the spiral starts in, which is how the Sq9 app measures them. The odd squares (9, 25, 49 …) all fall on the 315° diagonal.
More than one turn
Switch Turns to 2 or 3 to carry the levels further. The second turn's levels are the first turn's again, 2 further along the root, which is why the same angles keep coming back.
Questions
- What does a 'turn' mean here?
- One trip of 360° round the wheel, which adds 2 to the square root of the price. Two turns add 4, three add 6.
- Why are some levels gold?
- They sit on the cardinal cross (90°, 180°, 270°, 360°), the spokes traders usually watch first. The diagonals are blue.
- Can I look up a decimal?
- The levels work with any positive number. The spiral lookup needs a whole number, because only whole numbers have a cell.