This is the third and final article about the circular mapping of market swings via Fibonacci Arcs. In the first article we introduced this discovery as the missing link between the forecasting methods of W.D. Gann and R. N. Elliott. The second article discussed the Arc Principle in the context of Elliott Wave Theory. This article considers the methods originated by WD Gann, and it will show that Gann didn’t know everything there was to know about the squaring of price and time.

Many students of Gann have sought to make sense out of the apparent disconnect between Gann’s squaring of price and time and expressions of the Fibonacci ratio commonly associated with Elliott Wave Theory. There is no disconnect. The Fibonacci ratio was always integral to Gann’s methodologies, but neither Gann nor any of his students knew this. The connection cannot be found in the vertical and horizontal expressions of the Fibonacci ratio alone. One must venture into the circular world of Arcs to understand that the squaring of price and time and the Fibonacci ratio truly go hand in hand.

what gann didn't know

**1. Gann Angles are confirmed by Arcs.Gann Theory:** Gann used Gann Angles in two different ways. One way was as a gauge of the strength or weakness of the trend. If a market is trending close to a 1 x 2 angle, it is considered weak. If the market is close to the 1 x 1 angle, it is considered to be in balance. If it is close to the 2 x 1 angle, it is considered strong. The second way Gann Angles were used was to locate potential turning points. Gann’s adage was, “When time and price are in balance, look for a change in trend.”

“Angling for profits,” (below) shows Newmont Mining Corp. (NEM) with Gann Angles extending upward from the all-time low in 1978. Early on the stock penetrated the 2 x 1 Angle, which in theory means a stock is in a “strong” position, and in fact it was. But the investor would have had to endure years of uncertainty before the reading of strength came to fruition. Then there was the break of the 1 x 2 weak line in 1982. If it was now testing weak, was the prior show of strength eclipsed and no longer valid? No, as the market soon shot up like a rocket. The stock price again crossed over the 2 x 1 strong line in 1987. But if a trader took this as a sign that all was well and more highs were to follow, it would have been a big mistake. The stock plunged dramatically during the 1987 crash. The use of Gann Angles as guides to a stock’s strength can be misleading.

Gann’s other use for Gann Angles was to find actual turning points in the markets. If you follow the angle lines, you will notice several times when the stock touched a line and immediately reversed. If traded, more than half of these turning points would have been profitable.

**The Arc Principle:** “Arc angles” (below) adds a Fibonacci Arc to our NEM chart centered on the 1978 low with its radius set to the 1981 high. The 1.618 vibration (the larger circle) intersects the 1990 low on its perimeter at the precise moment of the turning point. This was the starting point of an upward move that continued for years.

The correspondence between Arc and Angle was no accident; it is a rule under the Arc Principle, which says to center the arc at the apex of the Gann Angle. To find a tradable turning point at a Gann Angle you set the base circle to an obvious swing that connects to the apex. From the base circle, add additional circles, or “vibrations” based upon Fibonacci multiples or fractions of the base circle. Then look for points where the arc and angle intersect at a turning point. The arc (inclusive of all Fibonacci vibrations) can intersect the turning point either on the perimeter of a circle, or in time, at the farthest right edge of a circle’s circumference.

(All charts used are scaled so as to relate the number of time units to price, based on the power of 10.)

**2. It is not just "Alpha"Gann Theory:** Gann Angles may tell you when to get into a trade, but do not tell you when to get out.

**The Arc Principle:** Not only does the Arc Principle tell you when to enter a trade at a Gann Angle, it also tells you when to exit. We will call the initial entry point, “Alpha” and the end of the ensuing move, “Omega.” Omega does not necessarily mean the end of the overall trend has been reached. It is the end of a swing-related specifically to the geometry of the Gann Angle. Every apex from which a Gann Angle starts has a swing leading into the apex and a swing leading away from it. In most cases, one of these two swings will act as the radius of the arc that intersects alpha (via the base circle itself, or one of its Fibonacci vibrations). The other swing will act as the radius of an arc that intersects omega.

“Finding alpha,” (below) shows a Gann Angle fan radiating downward from the October 2015 low in Wells Fargo (WFC). The middle angle intersects the blue shaded low. The October low is also the center of a Fibonacci Arc in which the larger blue circle extends to the November 2015 high. The smaller blue circle, .618 of the October-November swing, marks the time of Alpha at its horizontal extremity. It is this confluence of arc and angle that indicates a tradable turning point may be at hand.

Assuming one were fortunate enough to enter a trade here, under Arc Principle rules, one would then look for the other swing leading into the apex to exit. The red arc in “Finding omega” (below) shows this other swing. The larger red circle, which is 1.618 of the smaller base circle, circles to omega in time.

**3. It is not just Gann Angles.****Gann Theory:** Gann developed a number of trading methods, roughly divided into two categories: (1) methods based on the price movements of the instrument being traded, like Gann Angles or Square of the Range, and (2) calendar-based methods based on natural time cycles, such as the squares of 90, 52 and 144.

**The Arc Principle:** Unbeknownst to Gann and his followers, most all of Gann’s trading methods have a hidden arc component. Those methods that are based on price movements typically will show a Fibonacci Arc based on a market swing. Those methods that are based on the second category (natural time cycles) will have the radius set to that time cycle, but may also be confirmed by a market swing.

“Squaring price and time with arcs” (below) illustrates the time cycle category, using Gann’s Square-of-90. The Square-of-90 is based on 90 calendar days and is often a real force in the markets. The square at the chart bottom is one Square-of-90 (it works at any major turning point.) The radius of the smallest circle is set to one side of the square and acts as the base circle for the arc. If one were just working with arcs, one could have assumed that the genesis of this arc was the swing from the January 2016 low to the pink-shaded February 2016 high, or the swing ending at the April 2016 high. But in fact the arc was set based on the Square-of-90.

The correspondence of the Arc (inclusive of all circles) to the February, April and June highs is beyond dispute. But we can go further, for there was also confluence of the horizontal time of the smallest 161.8% blue circle and the perimeter of the 423.5% blue circle at the June 2016 double top. Of course, the largest blue circle had previously indicated the April 2016 high as well.

### Arc principle affirms gann

There is no evidence to suggest that Gann knew the significance of Fibonacci Arcs. But rather then represent a challenge, the Arc Principle validates Gann’s work. My research suggests that a seamless blending of the geometry of arcs with many, if not all of Gann’s methods, including the Square-of-9 (Gann’s most powerful tool) is possible. One need not venture into the Gann studies in order to trade via the Arc Principle, but those who wish to do so will find it a rich territory for exploration.