The Dow has had quite a rollercoaster ride ever since the previous all-time high of 11,750.28, back in January of 2000. This January marks the 12 year anniversary, which is 12 squared months (144 months), an observation that will come in handy a few charts from now. What a great time for a large-scale geometric perspective.

Can we fit the market into a geometric shape? And where and how would we start? How about at the very beginning of this big mess: the initial down trend from the previously mentioned high in Jan ’00 to the major low of 7197.49 in Oct ’02, expressed as a vector from high to low. All predominant reversals since are geometrically related to this vector, as we shall soon see.

The first chart shows the market conforming well to a large pentagon drawn from this vector (for a detailed breakdown of the actual technique of drawing this, skip to the end). The low of Mar ’09 is captured by the pentagon’s external circle. The time of the general support area of June ’10 (point 4) is indicated by the lower right corner. The upper right edge provides general resistance, although price is finally poking its head out. This helps to identify that current price action is at a very crucial point. A real break-out of this shape could be interpreted as a strong bull market with the above external circle and 45 angle providing potential resistance, while a reversal here could establish an important rally top.

The top of last May and current price are not just at pentagonal resistance, but directly at specific angles from the upper right corner of the pentagons’ surrounding rectangle. Notice that 36 degrees is a pentagonal angle (the upper sides of the pentagon are also 36 degrees from horizontal), and thusly, current price is at a harmonic AND thematic location.

In addition, by turning the internal pentagonal angle of 108 degrees into a time count in months, we arrive at points A (Jan ’09) and B (Jul ’10), both 108 months from the vector high and low, respectively. Both points are exact reversals: more support for a pentagonal approach.

The second chart shows the shear elegant power of the 45 degree scaling ratio, a true 1×1 relationship, as dictated by the 72 degree vector ratio. It reveals all important highs and lows as being connected via 45 degrees, but again, only shown in this particular fashion by aligning the initial vector at 72 degrees. Aligning the vector to other important degrees/shapes, such as 60 (hexagonal) or 45 (square), reveals important relationships as well, but I digress…..

If the Dow successfully breaks the pentagon in the first chart, I would use the ascending 45 degree channel for S/R. General resistance for Feb-Apr is 13,300 – 13,400.

The third chart is a necessary precursor to the fourth chart that clearly shows the relationship between actual time movement and percentage retracement levels of the pentagon height. Points 4 & 5: the vector’s 33 months, along with the 77 months between the vector low and the Mar ’09 bottom, identify the low and high of the previous up trend from Jul ’10 to May ’11 when expressed as retracement levels. These reversals are also harmonic with other major turning points using additional multiples of 11, at points 3 & 6.

The uses of trigonometric functions (ratios of triangular proportions) of pentagonal angles can work with alarming accuracy. At points 1 & 2, the sine’s of 72 and 54 (inverse of 36) degrees work well, identifying the all-time high with the main angle 72’s sine (.9511), and an important rally top at the sine of 54 (.809) which crashed the market (incidentally, 809 is 5 x 1.618).

All of these relationships clearly indicate that we are on the right track. But is there a harmonic explanation for current price? And what about timing points, since price techniques can be used for time as well?

The fourth chart reveals that current price is indeed at a junction of price and time. The fractional price level of ¾ is an interesting number: 12,722.72, (regarding 72 degrees), and is thematic with the other fractional levels of 1/10 and 1/3 (a.k.a 33%), providing accurate bottoms in Mar ’09 and Jul ’10 and even back as far as Oct 2004 (point 1). In addition, current price is at a fractional time point of 5/6. 3/4 price meets 5/6 time. This is a great location for a reversal, but certainly NOT a sure bet. Wait for confirmation, like a reversal candle pattern. If this resistance point does not hold, the market must have a lot of oomph!

This chart also reveals a ‘harmonic history’, regarding the 1/3 price level and its harmonic counterparts of 1/3 and 2/3 time points. At point 1, an important reversal formed exactly in price and time. At point 2, a potential top is foiled after the level is reached perfectly in time (2/3), then holds as support later on. Either of these two dynamics will play out currently. Just looking back in time….

Another clue to the power of the current time point of 5/6 is that it also aligns with 12 squared, 144 (remember?). In and of itself, this number has potential, as 144 is double 72, the pentagonal angle of the day, and both are naturally 2/5 and 1/5 of 360 degrees respectively. But when the squares of 4, 7, 10, and 11 also provide exact reversals, it has added weight.

Notice that the timing point of the sine of 33 degrees is 1 period from the all-time high. The sine of 33 will come in handy soon.

The fifth chart expands on the square numbers count from the previous chart. By geometrically relating the low of 11 squared on Feb ’10 with current price at 12 squared, they can be seen in a larger context of matching geometric relationships. The major highs at points 1 & 2 are perfectly connected to their major pullbacks (the pullback on Oct ’02, although not the lowest low, is very important, due to the extent of its retracement, and the almost vertical climb emanating from it) as these two lows vertically square with the vector high of 11,750.28, then proceed 45 degrees NE to the highs. Point 3 shows a smaller low (but impressive none-the-less) which gives the matching powerful rally-top of Mar ’08. This gives weight to a similar relationship forming at point 4, and supports the notion that the Dow is forming a secondary rally top, with a strong move down to follow. As noted before, a break of resistance at this crucial point would be very revealing.

Next, a 3 chart series demonstrating the power of the circle is presented (for great circle work, check out Michael Jenkins). These circles emanate from the initial vector at 72 degrees, and thus reveal relationships only seen from this relative perspective.

In the first chart of the series, the initial vector circle (blue) reveals harmonic vector distances to both the high of May ’06 (at 66 degrees), and the low of Jul ’10 (30 degrees). It is interesting to note the specific angles: 66 is double 33 and 30 is 1/3 (33) of 90 degrees. Secondly, the use of the sine of 33 (which gave us the all-time high area in the fourth chart) is used as an extension ratio, by adding it to 1. The all-time high did manage to poke its head out and look around, and so perhaps current price is just doing the same. The intersection of 45 degrees with the initial circle provided a bottom area on Feb ’09 (although the actual low was in early March, February had the lowest close). This indicates that the next intersection this July is a contender for a strong reversal. The second chart in this series displaces the circle by moving its center from the vector low to the major low of Mar ’09. It is a ‘graphic calculator’ of sorts, a measuring tool based on the initial vector. The top of Apr ’10 is this same vector distance, just at a different angle of ascent. This circle’s extensions of 1.33 (there’s ‘33’ again) and 1.618 (the Fib ratio is abundant in a pentagon) are telling. Notice how close the

actual price levels of the tops of these circles are to tops (in two cases, less than 3 points away). Once again, current price is hitting major resistance offered by the 1.33 circle and its top.

The third chart in this series is the gold (hey, speaking of gold, skip ahead to the last chart…). The initial vector circle (blue) has been displaced upwards to the first pullback (3-point low) in Jul ’09, immediately identifying the May ’10 top at 11 degrees. The up trend from the previous chart was at 7 degrees, and 7 + 11 = 18 which is the inverse of 72 (of course 7 & 11 are for a different paper altogether). Current price is hitting resistance at 16.5 degrees, which is a 1.5 ‘extension’ of 11 (11 x 1.5 = 16.5). Yet another harmonic reference to current price action.

If price successfully breaks resistance, the above red circle is the next resistance, provided by the next low in the up trend, on Jul ’10 (exactly 1 year after the previous low used). Successive measured moves from circles.

The next chart shows no less than 7 measured moves (circular), and I even left out a few. In other words, the initial down trend (vector) has been repeating ever since it formed, and still is!

The next two charts give a weekly perspective using the massive downtrend from the all-time high, aligned to (any guesses?) 72 degrees. 7728.15 points of destruction over 73 long months yields a VR of 105.865/W, and dividing by tan72 (3.0777) gives the 45 degree scaling ratio (1×1) of 34.3976, which rounds up to 34.4/W. (Refer to the procedural explanation at the end) The initial vector circle provides resistance (AGAIN!?!) for current price. A 45 degree angle from the lower left corner provides general ascending resistance, as well as ‘squaring out’ with the vector high in-between the weeks of Jan 23 & 30. Price and time meet here again.

Interesting to note that the first pullback in the up trend on July 6, 2009 is 18 weeks from the vector low (in degrees: 18 + 72 = 90), and squaring with the vector low and careening 45 degrees NE gives proper support for the important Oct 3 2010 bottom. Once again, a 45 degree channel rises and gives effective S/R, offering a glimpse of possibilities if resistance does not hold.

In the next weekly Dow chart, the sine ratios of the entire pentagonal angle series (18, 36, 54 & 72) are used for S/R levels in the vector price range. The ratios are as follows: .309, .5878, .809 and .9511 respectively. Retrospective confirmation of price’s involvement with these levels is given at points A & B, clearly defining the first rally in the initial down trend. And, as expected, they define three very important top areas, which are spaced according to the sine functions of pentagonal angles!?!

In addition, the two major tops are at the intersection areas of the 45 degree angle from the vector’s SW corner. Both the major bottoms occur either at or above the intersections with the lower 45 degree channel, with the next points being Aug 27 – Sep 3, 2012, and Apr 8, 2013.

And finally, we narrow down to the daily chart. The May 2 high of 12,876 to the Oct 4 low of 10,404.50 is 2471.50 points over 108 trading days (yes, 108!!). We get an initial VR of 2471.50 / 108 TD = 22.8843/TD, and then divided by tan72 (3.0777) we arrive at 7.4355/TD for 45 degrees and our scaling ratio. (Again, check out the procedure section at the end.)

Our last Dow chart clearly shows the sine of 72 at 12,755.04 retrospectively giving resistance in the initial down trend, as well as holding for current price (as of Thursday, Jan 26). A reversal candle pattern is forming at 45 degrees from the square point of tan36 (.7265) as well as from 72 degrees up from its inverse point (1 – .7265 = .2735) which picks off the high. Intersections for timing points work as well. This creates a massive focal point, seen through pentagonal geometry and trigonometry.

Conclusion: Monthly, weekly and daily pentagonal analysis provides a clear reversal area in price and time. As stated before, this is in no way a guarantee, just a high probability. If the Dow manages to take out all these harmonic relationships, there must be a LOT of force underway. In that event, circular and channel geometry can help guide the way.

And now for dessert: here’s a 32 year gold pentagon. Interesting to note that the pentagonal (5-sided) width of 470 months x the square root of 5 (2.236) is 1050.95. When added to the vector high of 873, gives 1923.95, exactly 25 cents above the all-time high of 1923.70. Sound odd (pun intended)? 25 is 5 squared! Goodnight.

Method for drawing the pentagon: The vertical scale is adjusted so it is seen at 72 degrees (this is easy to do after the 45 degree vector ratio is calculated, as shown below, by using a right-angle tool on the screen, if your charting program does not have a locking ratio feature. The calculations for the vector ratios necessary are shown below.

(Procedural note: If performed in a traditional geometric environment (an ideal scaling ratio of $1 week, or 20 points/month etc.) a pentagon drawn from this vector would not be set at 72 degrees from the vertical, would not point straight up, and therefore offer different points in price and time, however certainly effective. In other words, this vertical pentagon is an

actual perfect geometric expression of this very down trend. There-in lays its power. I refer to this type of approach as ‘Relative Charting’, since it is price action itself that determines the actual price to time relationship (scaling ratio), as seen from 45 degrees.)

The initial down trend’s vector ratio (‘VR’) is:

**72 degree VR = 4552.79/33M = 137.963/M**

(Interesting to note that this figure is almost exactly 138, which is 72 + (33 x2), as in 72 degrees and the vector’s 33 months, as if price is telling us that 72 and 33 are very important)

**45 degree VR = 72 degree VR / tan72 = 137.9633 / 3.0777 = 44.827/M**

(Also worth noting is that the 45 degree VR is almost exactly 45!?! so far so good)

Next, the base length can be determined by calculating the vector length as a hypotenuse of a right triangle, which involves converting the price movement of 4552.79 into months by dividing it by the scaling ratio of 44.827, resulting in 101.56M (side a), and combining it with 33M (side b) using the Pythagorean Theorem:

**(101.56)(101.56) + (33)(33) = 11404.16 = (106.79)(106.79)**

The length of the hypotenuse is 106.79M, rounded up to 107 (almost 108). So draw a horizontal line 107 months from the vector low to Sep 2011.

From there, draw upward 33 months to the right, and connect with the vector high of 11,750.28. This naturally gives you a 72 degree line. The pentagon is technically 172.79M across (33 + 106.79 + 33), and rounded up to 173M, at June 2014.

Next, calculate the pentagon’s top price by either dividing the vector range by .618 (giving 7366.974), or multiplying it by the Fibonacci expansion 1.618 (giving 7366.41). They are slightly different results, yet I see the logic in both approaches. The monthly charts presented opt for the first approach, which is ‘top-down’ (so to speak) and yields a price of 14,564.50.

Connect both the vector high and its right-sided counter-part point to this top price at ½ of 106.79M from the vector low which is 53.40M (rounded), right in-between March and April 2007.

For the external circle, locate the center of the pentagon by multiplying the height by the center ratio of .4472, and add it to the vector low:

**7366.974 x .4472 = 3294.51 + 7197.49 = 10,492 center height**

Draw a circle from this center until it conforms to the pentagon’s points. Also, try an internal circle, which touches the mid-points of the sides.