24 Levels into the Bubble Core

We have been exploring the interesting properties of the Bubble Core. Looking at circles from a slightly different perspective. Mapping out mathematical and physical behaviors. We already know interesting things happen within the core. What happens when we drill 24 levels into the core. How do we even do that?

Let’s break down how the Bubble Core equations work. First we setup a boundary in which will have a Base and Limit. In the case of a circle you can think of the Base as being 1 circle and the Limit has being 4 quadrants.

We further define what I am calling Size and Scale for now. The name of these variables may change but for now we will stick with it. Size (p) is how we adjust the actual size of the circle in this method, rather then defining the radius with a hard value. You can also see if you wanted to define the radius first as we commonly do we could define the following equivalent method.

Thinking about a circle this way allows us to understand the polarity of a circle. The hemispheres and quadrants that are natural to a circle of any size.

I have talked about how this is all the identify of what I call OctoQuadrian Numbers. These numbers numerically have a bizarre circular patterns that mirror what we are seeing geometrically in coordinates.

To fully understand how the Bubble Core Levels work we need to look at how the angles would be determined for the various levels. What are the underlying mathematic and geometric mechanics that govern the size of a core at each level. To explore this we setup the following .

This allows us to change the value of n to produce 3 angles. We further find that setting n=850 gives us the precise angles required for Level 1. Why 850? This is where things really start to get more interesting. It turns out n acts like a multiple of 360.

This suggests that every core level will be with in the range of 850 through 1440. When viewed as a multiple of 360, the range for the Bubble Core Levels starts at 2.3611 and less than 4.

It is here I am going to classify 3 types of angles to apply to this same method which will allow us to really explore what is going on. The first I call Keystone Angles. These are angles produced by whole number multiples of 360. The second are Primary Polar angles which I have discussed in the past. Finally the third are Bubble Core Level Angles. This is not to be confused with the Bubble Angle of 120 degrees.

Drilling in 24 Levels into the Bubble Core we find some very interesting patterns. We do in fact see that the cores are within the range I had suggested earlier. We also see the changes to the value of n become incredibly small with each core level. Its seems like it will eventually converge on 45 degrees but you can see something very interesting happening when we plot the actual Bubble Core Level Angles.

What can Primary Polar Angles tell us? Remember, Polar Angles are any whole number angle that reduce to a digital root of 9. The Primary Polar Angles are based on initial polar pairs from the Sequence Map.

We find the Golden Ratio yet again hiding in the math of the Bubble Core. This time it is a little different and exact!

“Coming full circle” in this case is more than just a pun. It is literal. We need to talk more about Pi and SyPi. We have already found Pi many ways over embedded into the bubble core. Both as a Circle and a Square. I have suggested that Pi may not be the static number we claim it to be. In fact when we measure it it is always an approximation. I have demonstrated multiple times how SyPi can produce much more accurate results. I have suggested Pi is a Gradient that fluctuates based on the context.

The following is yet another indication that this could be correct.

Here again we find the accepted value of Pi is close but not as close as it could be. This equation seems so perfect for Pi to solve perfectly but it doesn’t. Something to note about the SyPi position -75.162 and what that could mean. It turns out that the decimal if repeating could equal exactly 850.

The very first level of the Bubble Core is tied to an equation using Pi which is made more accurate by using SyPi. This is extremely interesting in the context of everything I have ever said about Pi.

Again you don’t have to take my word for it. I set up various models and examples on GeoGebra for anyone to try and see for themselves.

SyPi
https://www.geogebra.org/m/xrffzsng

Bubble Core
https://www.geogebra.org/m/hg5pyjgt

Bubble Core Angles
https://www.geogebra.org/m/ahsfhx7w

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Stay Tuned.

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