Cosmic Numbers

We can write down our number (x) and its reciprocol (1/x) in a single equation.



And we can always seperate these numbers, as shown :




It is assumed that (x) is always ≥ 1 and the (1/x) is always ≤ 1.


The following 'cosmic' numbers are interesting, because the number (x) minus its reciprocol (1/x) equals the numbers 1-9.




The following 'cosmic' numbers are interesting, because the square of the number (x) minus the square of its reciprocol (1/x) equals the numbers 1-9.




The following table shows these numbers in decimal, and how they interact with this interesting mathematical cosmic identity.







Metallic Means

Each cosmic number has a corresponding sequence of numbers, as you can see the first and second sequences are called Fibonacci and the Pell sequence. These sequences are known as the metallic means or silver means.


As you can see below, as these sequences approach infinty, the ratio of the last two consecutive numbers tends towards the number (x).




As you can see below, as these sequences approach zero, the ratio of the last two consecutive numbers tends towards the number (1/x).




The following table shows the (approximate) Major/Minor ratios.




The Number 4


Below we can see the importance of the number (4) Trying to simplyfy..



The Golden Ratio

The most interesting of all the cosmic numbers is the golden ratio (ϕ) and out of it come two very important number sequences, Fibonacci and Lucas.




The green number sequence (Tribonacci, Tri-Fibonacci) is created by simply adding a yellow Fibonacci number to a blue Lucas number, as shown below.



We also find this sequence, which has become known as Binet's formulas. It shows the amazing relationship between the Lucas and Fibonacci numbers and the golden ratio (ϕ) .


To be continued...

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