**not**unforseen.” From the age of 24, the Sqaure-of-9 — a sequence of orderly numbers spiralling outwards in an anti-clockwise manner from the number 1 at the centre (Figure 5) — generated him $50 million from trading stock and commodity markets.

*“I soon began to note the periodical reoccurrence of the rise and fall of stocks and commodities. This led me to conclude that natural law was the basis of market movements. I then decided to devote 10 years of my life to the study of natural law as applicable to the speculative markets and to devote my best energies toward making speculation a profitable profession.” *

The numerals 1-9 forming the Square’s first ring inspired him to coin the device ‘The Square-of-9’, and its geometrical divisions, cardinals and diagonals.

The Australian mathematician, physicist and meteorologist, Trevor Casey — the first known man to unravel the Square’s mathematical structure since Gann — points out that all the Square’s Internet versions are mathematically wrong. In *The Square Spiral— the Mathematics of Markets (BookPal 2010) *he* *explains that this Square is a spiral mimicking the Milky Way. As such, it unfolds from left to right, in the same direction as the galaxy, and each of its rings expands twice during one 360^{0} revolution. The first expansion takes place upon the Square’s north-western diagonal and second upon its south-eastern arm. Therefore, in contrast to the Internet versions, the north-western diagonal runs along the numerals 1, 2, 10, 26, 50…**∞**, and the south-eastern along 1, 5, 17, 37, 65….…**∞.** (Figure 5)

The other point he emphasises is that the Square is a calculator designed to measure time and should not be used in forecasting price levels. The 0.618 and 0.382 Golden mean proportions, known as Fibonacci ratios, are best for determining the support and resistance levels of price.

**Figure 5** – The Square-of-9 constitutes a spiral of consecutive numbers unfolding outwards from the number 1 at the centre. Its numerals follow the anti-clockwise (left to right) direction of the Milky Way’s spiral.

Gann’s breakthrough came about when he observed that time-intervals typically adhere to the Square’s axes in that they commence and terminate upon them. A mature interval bounces off and culminates upon the Square’s same axis by completing a 360^{0} rotation from and back to the point at which the preceding interval ended. In cases when a swing terminates upon the Square’s opposite axis, at 180^{0 }angle, it remains unfinished until such time it completes a 360^{0} rotation to the axis it had bounced off. Given that the present recovery wave took off the Square’s eastern cardinal, and must terminate upon it, the Square-of-9 makes is possible to forecast its maturity date.