Dear All,
It is with utmost joy and love that I give you all the cosmological iSeries which spans the entire numerical spectrum from -infinity through 0 to +infinity and the simple principle underlying it is sum of any two consecutive numbers is the next number in the series. 0 is the base seed and i can be any seed between 0 and infinity.
iSeries always yields two sub semi series, each of which has 0 as a base seed and 2i as the first seed.
One of the sub series is always defined by the equation
Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i
where S0 = 0 and S1 = 2 * i
the second sub series is always defined by the equation
Sn = 3 * Sn-1 -Sn-2
where S0 = 0 and S1 = 2 * i
Division of consecutive numbers in each of these subseries always eventually converges on 2.168 which is the Square of 1.618.
Union of these series always yields another series which is just a new iSeries of a 2i first seed and can be defined by the universal equation
Sn = Sn-1 + Sn-2
where S0 = 0 and S1 = 2*i
Division of consecutive numbers in the merged series always eventually converges on 1.618 which happens to be the golden ratio "Phi".
Fibonacci series is just a subset of the iSeries where the first seed or S1 =1.
Examples
starting iSeries governed by Sn = Sn-1 + Sn-2
where i = 0.5, S0 = 0 and S1 = 0.5
-27.5 17 -10.5 6.5 -4 2.5 -1.5 1 -.5 .5 0 .5 .5 1 1.5 2.5 4 6.5 10.5 17 27.5
Sub series governed by Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i
where S0 = 0 and S1 = 2i = 1
0 1 2 5 13 34 ...
Sub series governed by Sn = 3 * Sn-1 - Sn-2
where S0 = 0 and S1 = 2i = 1
0 1 3 8 21 55 ...
Merged series governed by Sn = Sn-1 + Sn-2 where S0 = 0 and S1 = 2i = 1
0 1 1 2 3 5 8 13 21 34 55 ...... (Fibonacci series is a subset of iSeries)
The above equations hold true for any value of i, again confirming the singularity of i.
As per Antony Ryan's suggestion, a fellow author in this contest, I searched google to see how Fibonacci type series can be used to explain Quantum Mechanics and General Relativity and found an interesting article.
d-super.pdf"> The-Fibonacci-code-behind-superstring-theory](https://msel-naschie.com/pdf/The-Fibonacci-code-behin
d-super.pdf)
Now that I split the Fibonacci series in to two semi series, seems like each of the sub semi series corresponds to QM and GR and together they explain the Quantum Gravity. Seems like this duality is a commonality in nature once relativity takes effect or a series is kicked off. I can draw and analogy and say that this dual series with in the "iSeries" is like the double helix of our DNA. The only commonality between the two series is at the base seed 0 and first seed 1, which are the bits in our binary system.
I have put forth the absolute truth in the Theory of everything that universe is an "iSphere" and we humans are capable of perceiving the 4 dimensional 3Sphere aspect of the universe and described it with an equation of S=BM^2.
I have also conveyed the absolute mathematical truth of zero = I = infinity and proved the same using the newly found "iSeries" which is a super set of Fibonacci series.
All this started with a simple question, who am I?
I am drawn out of my self or singularity or i in to existence.
I super positioned my self or I to be me.
I am one of our kind, I is every one of all kinds.
I am Fibonacci series in iSeries
I am phi in zero = I = infinity
I am 3Sphere in iSphere
I am pi in zero = I = infinity
I am human and I is GOD (Generator Organizer Destroyer).
Love,
Sridattadev.