The previous essay indicated the math according the first formulation of twin cubes did not seem to work out as expected and that both cloned ellipses and an alternate formulation of the twin cubes suggests a final new all-time high in DJIA on about April 27, 2017 at above DJIA 22000. The latter suggestion of a new all-time-high was based on a visual fitting of the 2000-09 square ABCD and has been updated by a more, but not entirely, mathematic triangulation of point E (the suggested final all-time-high) at DJIA 22300 on May 2, 2017. Again, this revised calculation is a better "biangulation" of point E but remains not entirely mathematic in its derivation. Here's the revised chart:
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What early tip-offs did I have that March 1 was not the final top for the 2000-17 cube? First and as previously noted, I should have recognized, by my own chart, the cloned cubes B and C axes did not form a perfect, overlapping straight line with their enveloping ellipse A:
Second, I should have noticed from my own chart of the period 2009-present, not previously shown, has some imperfect math:
Sectioning PTV's CE and DE according to the intersection of the 2007 price high and actual price results in components of those vectors that appear to be edging closer and closer to ideal root 3 and root 2:
But they have not reached root 3 and 2 ideals...yet. Recall the mathematic significance of root 3, the center diagonal of the 1X1X1 cube (3 dimensions) and root 2, the diagonal of the 1X1 square (2 dimensions). By establishing a new higher high in the not distant future, the subdivisions of CE and DE will inch closer to the Platonic ideals.
Isn't this intuitively attractive according to WD Gann commentaries on how we expect "vibration" to reach its mathematic extreme before some new shock or impulse or predetermined mathematic extreme reverses the market?
I should have known earlier, that a marginally new high is needed to perfect the math. It was the loose thread at that moment that I did not follow. Now, is the point E I seek, the newly identified point E at DJIA 22300 on May 2, 2017? That's my best "biangulation" at the moment.
Still working on the math. I expect a still finer point E projection and math that will support (or refute) the model of the market structure shown in the chart at the very top of the page.
And then the question will become, what is the correct point F...the next pivot bottom counterpart of point E top?
Jim Ross