Gann Wheel and Ulam Spiral

The Gann Wheel, also known as the Square of Nine, a computational tool useful in the financial markets:

The Ulam Spiral, a graphical representation of prime number distribution.

Apart from both starting with one as the origin and spiraling out from the center, what mathematical relationships exist between the Gann and Ulam?

Suprisingly, Googling “Gann” AND “Ulam” yielded no results.


As you are observing, the arrangement of numbers on both are the same sort of spiral, with minor differences in where the start of the spiral is positioned, and direction. The “Square of Nine” you have shown illustrates what type of relationship diagonals and rows or columns of the spiral actually have. Each of the “rays” is a sequence generated by some second degree polynomial, which you can readily see by taking differences, and which makes perfect sense when you think about how the spiral is constructed. For example:

1 3 13 31 57 91
2 10 18 26 34 <- degree 1
8 8 8 8 <- degree 2

The Ulam spiral indicates that a lot of primes seem to be generated by certain second degree polynomials. Seem may be an important word here, as the polynomials in question are obviously not exclusive generators of prime numbers, and humans are notorious for seeing patterns in random data.

I can’t find any information about how the Gann wheel is constructed. Got a link?

The pictured spiral is the same as the Ulam spiral, except that it spirals clockwise instead of counterclockwise, and he begins spiraling from the cell to the left of the 1 rather than the right. We should be able to come up with an expression for the number in the cell located at given coordinates but I don’t feel like thinking about it right now.

Another description:

Why stock traders think there is any significance to patterns of prices in relationship to the thing is another topic of course.

You’re not likely to find any deep relationships between the Ulam Spiral and the Gann Wheel because the former is actual mathematics, whereas the latter is pure numerology (i.e., bullshit).