It’s time to revisit Syπ and what it means for π and other constants.
I had said in my last post, that my next would be about light. I have to hold of that for now to explain more about Pi and SyPi.
The connections I have described between the Fine-structure constant, Golden Ratio and Pi are hard to ignore. What is really interesting is when you step away from our limited but comfortable understanding of Pi to look at from a different perspective.
The SyPi Equation is a completely new way to think about Pi. It is obvious to anyone with experience using Pi that 180/Radian equals Pi. In all of my discussion about SyPi, I have failed to really highlight the unique method to which the Radian is derived putting more emphasis on SyPi itself or the Gradient function.
This post I am going to correct that. I will break Pi and SyPi down, highlight their differences and compare their behaviors in the real world.
We do in fact find Pi everywhere, not just in circles. We find it in probability theory, the swings of a pendulum, the length of a river and many other places that have nothing to do with circles. At least on the surface.
There are many formulas for Pi and many values have been “accepted” as official values of Pi over the course of history. Infinite series and geometrical techniques have been exhaustively tested over thousands of years before arriving at the current accepted value of Pi calculated to more than 31.4 trillion decimal places by the world’s most powerful super computers. This very much makes it seem like a given that we are in fact right about Pi, doesn’t it?
Well, when we measure and find Pi in that natural world what do we see? It is always seems to be an “approximation”. If we are right about Pi should we not see the exact value of Pi turn up more often. Especially when dealing with circles and spheres. We don’t, we get different approximations of Pi everywhere.
There are many others who have noticed the logical problems with way we view and calculate Pi. Norman Wildberger explains these problems in great detail. He suggests calling Pi a “meta-number”. He makes the argument Pi cannot be thought of in the typical sense because of it’s unique properties and logical challenges. That Pi is a different kind of mathematical object. He talks about it all in depth here: https://www.youtube.com/watch?v=lcIbCZR0HbU
Based on my research and discoveries I completely agree with him. Pi is a “meta-number” and I will demonstrate why.
I collected 20 “measurements” or “approximations to Pi as a start to an ongoing Pi VS. SyPi experiment. While this is only 20 for now, I think off the hop it is interesting to note that the “accepted” value of Pi only has 1 hit out of the 20. SyPi has 669 matches with multiple hits in 15 of the 20 values compared. One could make the argument that in this case SyPi is 75% accurate while Pi is only 5% accurate according to what we see in these initial 20 cases.
Okay, so lets break down SyPi into parts. That starts with what I call Problem #1. I have explained this in previous posts but will run through it again with a much better understanding of what is really going on. We want to create a formation of circles in a circular orbit in such a way that the circles kiss (touch).
Looking at the following constructions we find an equilateral triangle works perfectly for 2,3 and 6 circles in formation. 4 is a little different, than 5 comes up a little short, while 7 and above u ends up being higher.
This problem can also be viewed as a kind orbital problem. So far we have 5 key variables, to solve for r2.
WHERE p is the number of circles in formation. We will start with p=9
WHERE r1 is the radius of each circle. We will also start with r1=9
WHERE θ is the number of degrees in a circle.
WHERE n is the number of points in a triangle n = 3
WHERE u is either the gap or tale of r2 from center to center of each circle in formation.
I decided to use our moons orbital period of 28 days as another variable. The moon has an interesting orbit that is perfectly in sync with earths. So much so that we only ever see one side of the moon from earth. If this could in fact be viewed as an orbital problem it just seemed to make sense.
WHERE T is the orbit period T= 28
So now we have 5 variables to solve for r2 and this is where things start to get interesting. I do not want to shift focus away from Pi and breaking this down but I need to note it is here when I made an interesting discovery about the Synergy constant and a potential connection to the Radian. I found that 126/2.162 gave a result similar to the value of a Radian at 58.27937… It is a little higher than what we know to be the Radian at 57.29577. What caught my eye was that the difference between the two seemed to be about the size of the gaps between circles in formation and related to the u variable from my constructions.
To figure out if there was indeed a connection I set up three more variables to account for this interesting Radian like number.
WHERE Sb is the Base constant Sb = 126
WHERE Sl is the Limit constant Sl = 2.162
WHERE Rb is the Radian Base constant Rb = 58.27937095…
I setup another three variables to look at how this Rb is connected the u from the constructions.
WHERE u is the Radian Flux ( difference between Radian and Rb )
WHERE x is the ratio between u and r1.
Now we have 11 variables and we are closing in on potentially solving this problem. First we have to figure out how to put all these variables together. We know the length of r2 is directly dependent on the length of r1 and the total number of circles in formation p.
The 12th and 13th variables I added on a hunch similar to that of the lunar orbit period. I called it the Golden Reference initially because I expected the Golden Ratio/Angle to somehow be involved. This value was a little higher then the golden angle however and I later discovered is was tied to the Synergy constant. I also added the Synergy constant itself.
WHERE φ is the Synergy Polar Angle Reference φ = 222.222
WHERE S is the Synergy constant S = 162
Again I do not want to switch the focus to the Synergy constant, just note it’s significance. This may seem a little odd and arbitrary but follow it through.
It is here were I began to derive what I call the Radian Flux constant. I called it a flux because it controls the distance between circles in formation from center to center. I likened it to a tax on the the angle of r2 based on the value or p and r1. This constant that would calculate that tax.
We will use this constant to determine the total amount of flux or u in our construction. Calculate a ratio of the flux to r1 then subtract that ratio from the Radian Base constant.
This gives us a value that is almost exactly the commonly accepted value for a Radian.
This is essentially controlling the angle of placement but it is not exactly the same value as a common Radian. It was here I discovered SyPi. An approximation to Pi that was extremely close to the accepted value of Pi, matching the first 7 decimal places. This may not seem like much. There have in fact been a number of formulas that can calculate pi accurately.
What struck me as different at the time was how Pi just popped out so accurately and naturally from simply trying to break down and describe this problem in a geometrical and logical way. Not only did it lead to me solving the problem but I discovered that the Synergy constant in the Radian Flux constant was actually a position number resulting in a full gradient of Pi like values. When S is equal to 1 the value for Pi is extremely close to 22/7. When S is equal to 162 it is closest to the accepted value of Pi.
I finished solving Problem #1 with this new SyPi and it worked!
Not only did it work, it seemed to work exactly the same as using standard Pi. I found this interesting and wanted to compare every version of Pi in history, using this problem as a benchmark to test performance of each. I put up a page to run this test and set any number of circles and their radius. I included every accepted value of Pi I could find through out history. You can try it out here. https://synergysequencetheory/problem1
This test keeps iterating. Meaning, it keeps placing circles in formation over and over. There is a noticeable difference between all other variations of Pi VS. the current accepted value of Pi, SyPi. Pi and SyPi seem more stable in being able to handle the iteration.
Very interesting!
While researching connections to the Fine-structure constant and Golden Ratio, I came up with another way to pit Pi VS. SyPi and see which was more accurate. I call it Problem #2. I also wanted learn more about the Gradient of Pi values. What I call the SyPi Gradient.
You can check out SyPi and the SyPi Gradient with this WoldframAlpha link. Swap out different values of a. When a = 162 it is closet to the accepted value of pi. https://www.wolframalpha.com/input/?i=180%2F%28%28126%2F2.162%29-%28%289-%289*%28%28%28a*%283%2B%28%28%28%282%2F9%29*%2810%5E3%29%29%2F360%29%29%29%29*28%29%2F10%5E6%29%29%29%2F9%29%29
The solutions for these 2 problems are extremely compelling. I invite any one to test it out for themselves. It works! Not only does this all work, SyPi has proved to be more accurate than Pi in the following:
- Near identical behavior in Problem #1
- SyPi is more accurate in Problem #2
- SyPi has more hits in Pi VS. SyPi Comparison (Pi: 1/20 | SyPi: 15/20) *sypi seems more natural
- SyPi[173] is more accurate calculation of Fine-structure constant
- SyPi[173] is more accurate at calculating distance of Fine-structure to 45 degrees
I am still researching and learning new things about SyPi everyday. Of course as I have said it is in fact Pi we are talking about, just in a different way. No matter what, this all provides interesting insights into what Pi is beyond just some irrational number we can only ever approximate to.
I suggest based on all of the above that Pi is in fact a function. A gradient. It represents a fundamental unit regardless of how you measure it. It scales perfectly both big and small. I like the idea of calling it a “meta-number” as Norman Wildberger suggested to make clear that it is a very different kind of mathematical object.
The connections and patterns between these numbers and constants I have been pointing out are too many to simply ignore. I hope that clarifies why SyPi is different. My next post I will start to reveal the connections to light as promised. Stay tuned.
