AuT-pp: dimension examined 2 of whatever

There will be at least, probably two more posts from what has already been generated, but if you are patient, there will be more.  A few days isn't too long to wait for what you already know if you've read this.long enough or bought the books.
When you do a Geometric proof of d/dtheta(sintheta)=costheta

Y=sintheta (vertical postion of circular “motion”) you end up with a diagram like this.

In a purely linear universe, it is possible to get closer and closer to a quantum shaped curve, but this will not work in a quantum state universe  For this reason we know that we have a quantum state universe which gives rise to a linear state universe, the only question is how.

What’s interesting about this is that gap B (the gap between the straight line q-p and the arc is more narrow than, for example, A (the gap between q-baseline).  AuT, quantum theory suggests that at some point these changes must be quantum difference, that is they cannot be subdivisions requiring minimum lengths B and minimum line lengths p-q, for example.

 Looking at the angles above, it can be seen that a quantum lengths r and y have to be equal for a guantum length of the arc lengths but even then you end up with portions (like A an B) which are sub-quantum lengths but still defined by the quantum values of deltax and deltay.

There are other, more isolated ways to look at how is this problem solved, how do you get from quantum changes to sub-quantum changes, from yes/no answer to answers which appear to have dimension and smaller size?

This is not the way of AuT, but it approaches the method of AuT In order to see this we're going to look at a slightly different way of look at this, we're going to look at some isosceles triangles, the greek delta, a symbol of perfection, but not one of balance.

This shows another way to envision this process of stacking quantum states.  For purposes of this diagram, it will be assumed that the legs of the triangle are yes/no solutions.  This means they have no true distance.  They are, however aligned so they can be compared.  The first layer (the top triangle) is circular in a fashion but it's a lot different from our circle in a linear universe.  This is a quantum circle which not a circle at all.  If you look in the book (or wait for the next post) we'll get to 5 and seven sided equal sized objects, but wait for the moment.

Once start to stack these (and this is not, btw straight F-series stacking although the results are not so different) we begin to generate comparative pieces. which vary relative to one another even while the quantum lengths stay the same.

For example the "distance" or the "percent" of a quantum result C is smaller than b which is smaller than a.  You either have to change what makes up quantum distance, which screws up linearity as indicated above, or you have to look at the comparison between quantum solutions, this is another way of looking at the ratio of yes to no results.  In the triangle you have this and in the F-series 0,1,1 you have this.  You also see this at the 1,1,2 level, the last level that has this pure model although the 0,1,1 model is unique.

To get from the first triangle to a, from A to b or from b to c the size of the figure must grow sufficiently so that the edge of the triangle, a, b and c all have a minimum length and to get from one shape to the next some expansion is required in quantum length, but if you are only looking at one relative to another you don't have the same issues.
You can get the same results as the a, b, c results by comparing the number of 0 states to 11 states or, if you like, the 1,1 states to 2 states when you begin to stack.  In the case of the top it is 1 to 2 in the second drawing it is 2 to 4; in the third it is 3 to 6 but the potential exists at any location for this to be weighted as long as it evens out somewhere else.  But you also have 1,2,3 of the non-base state to 1 base state if the single triangle is a base.  This changes dramatically if you are going from 1 change at a time to two (1,1 to 11, 11)  at a time because the equation for change is 2^(2^2) for the base change to (2^2);4^(2^2);6^(2^3); and 10^(2^4) relative change ratios among others at the state where we find ourselves and the comparative states between these states is enormous whether localized or not.

For the derivation of pi you have a similar issue in reverse, but you still have a comparative analysis.

This is important because the one thing that stays true about this analysis is that the legs of the triangles all stay the same.  The comparative features of the triangle change relatively speaking, one to the other, and seem to require an infinite variation between minimum lengths, but this is illusory since the value of any triangle of quantum length remains constant, the quantum state of the universe is preserved while perceived variation in length or curvature changes.
It's important to see how these features arise, it is important to understand how the relativity this represents expresses itself as the reality we experience, the long and short, the fast adn slow, the light and the dark, it's important what it says to us and what we have to intuit from it.

https://www.youtube.com/watch?v=KMihKmoYfe8