42 Strings of the Diamond of the Universe & Sequencing the Squares

Howdy peeps,


In the sequencing order behind what’s known as the Diamond of the Universe, which has 42 Strings, the order is:

1-4-8-16-8-4-1

1 + 4 + 8 + 16 + 8 + 4 + 1 = 42

From that sequencing and in a one-way direction only, and not the additional flip of perpetual motion, the first 13 numbers are:

1
4
8
16
32
64
128
256
512
1024
2048
4096
8192
etc...

There’s an interesting factor of squares and the preceding numbers, as well as the other numbers in that sequencing, in that any square can be summed by using just those numbers above, and additional numbers in sequence, and never using more than one number once in each Squaring and never needing additional numbers. See the following:

1² = 1
2² = 4
3² = 9 = 8 + 1
4² = 16
5² = 25 = 16 + 8 + 1
6² = 36 = 32 + 4
7² = 49 = 32 + 16 + 1
8² = 64
9² = 81 = 64 + 16 + 1
10² = 100 = 64 + 32 + 4
11² = 121 = 64 + 32 + 16 +8 + 1
12² = 144 = 128 + 16
13² = 169 = 128 +32 + 8 + 1
14² = 196 = 128 +64 + 4
15² = 225 = 128 + 64 + 32 + 1
16² = 256
17² = 289 = 256 + 32 + 1
18² = 324 = 256 + 64 + 4
19² = 361 = 256 + 64 + 32 + 8 + 1
20² = 400 = 256 +128 + 16
21² = 441 = 256 + 128 + 32 + 16 + 8 + 1
22² = 484 = 256 + 128 + 64 + 32 + 4
23² = 529 = 512 + 16 + 1
24² = 576 = 512 + 64
25² = 625 = 512 + 64 + 32 + 16 + 1
etc ... .. .

It continues to infinity, of course, and I was just wondering if anyone knows about that mathematical rhythm of the squares and how you can simply double 1 to infinity to get the 2X + 1 sum elements of the squares?

What does this planet call that?

Ribbit

 

WOW! You have figured how to convert numbers into binary.

 

Actually, what it is is the Even Steven Sum of Squares, wherein you only use even numbers to sum squares, except for odd number squares and with those you can use the odd number of 1 in the summing sequence but only 1 and you can only use a Even Steven Number once, in summing any square with Even Steven Numbers.

Whereas with Odd Claude Numbers, you only use Odd Numbers and in sequence to the number being squared.

1² = 1 (1 odd number)
2² = 1 + 3 (2 odd numbers)
3² = 1 + 3 + 5 (3 odd numbers)
4² = 1 + 3 + 5 + 7 (and so on ...)
5² = 1 + 3 + 5 + 7 + 9
6² = 1 + 3 + 5 + 7 + 9 + 11
7² = 1 + 3 + 5 + 7 + 9 + 11 + 13
8² = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
9² = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17
10² = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
11² = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21
12² = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
13² = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25
etc ... .. .

With Even Steven Numbers, you use fewer numbers and you never use the same number twice in one squaring but the Order isn't as perfect and while the base numbers are all Even Numbers except for the Number One and it is only used in Odd Number Squares, with Odd Claude Numbers, the Order is perfect but you use more numbers and you never use a single Even Number, always Odd Numbers, and just like with Even Steven Numbers, you never use a Number twice in any squaring with Odd Claude Numbers.

Ribbit

 

Ps: What it is also is RLM is two ways of proving you can answer the Sum of Squares with either all Odd Numbers or All Even Numbers and it also works with never using a number more than once in each summing and when using Even Numbers for summing, when it comes to odd base numbers, the Number "1" is allowed in the summing sequence but it's the only odd number allowed and you can only use it once in the sequence and only when the base number being squared is an odd number.

But you can answer the sum of squares with odd numbers only instead and never have to use an even number in the computation.

Odd number summing is easier to understand and predict but even number summing keeps the clutter down and is mathematically organized better and is more flexible in its nature.

Ribbit

 

Here's another bi-versal primer situation that's similar.

Rule of 8 by 2 by 9 Numbers Puzzle

The Rule of 8 by 2 by 9 Numbers Puzzle is just a play on numbers but it also gets into .9 to infinity equals 1, which is a correct mathematical concept when it comes to Closed System Math but that concept is wrong when it comes to Open System Math, but that’s another matter; nevertheless, this Numbers Puzzle should spark your curiosity as to how it all works, if you will just dew the math and the answer to this puzzle explains the math of Marko Rodin’s Number Puzzle, which, in turn explains the math of Vortex Based Mathematics and its Octal Nature.

The Rule of 8 by 2 by 9 Numbers Puzzle demonstrates an intriguing second method to do the math with an Infinity Rule of 9 situation and it does so twice.

The Rule of 8 by 2 by 9 Numbers Puzzle is based on the Infinity Rule of 9,
which can be shown easily:

1/9 = .1 to infinity
2/9 = .2 to infinity
3/9 = .3 to infinity
4/9 = .4 to infinity
5/9 = .5 to infinity
6/9 = .6 to infinity
7/9 = .7 to infinity
8/9 = .8 to infinity
9/9 = 1
Etc….

The Rule of 8 by 2 by 9 is quite simple how it works. The first method is to double 8 to infinity, then to divide each result by 9 and the result of that is known as the Proofing Answer, which is used to verify the answer you get when you do the math the other two ways:

16/9 = 1 with a remainder of 7 = 1.7 with the 7 to infinity
32/9 = 3 with a remainder of 5 = 3.5 with the 5 to infinity
64/9 = 7 with a remainder of 1 = 7.1 with the 1 to infinity
128/9 = 14 with a remainder of 2 = 14.2 with the 2 to infinity
256/9 = 28 with a remainder of 4 = 28.4 with the 4 to infinity
512/9 = 56 with a remainder of 8 = 56.8 with the 8 to infinity
1024/9 = 113 with a remainder of 7 = 113.7 with the 7 to infinity
Etc….

The first method is used primarily to help prove the second method and while the second method is similar to the first, the difference is in the bi-versal method used to manipulate the numbers but that’s because the primer for the Numbers Puzzle uses 2 different forms of math instead of the common/normal single verse primers. The procedure for the second method is:

Where X = (8 multiplied by (2 to I)) . . . Divide X by 9 to get the whole number portion of the complete answer, then divide the whole number portion by 8 then subtract the remainder of that partial answer from 8 to get the decimal infinity number, then combine the whole number partial answer with the decimal infinity number partial answer for the complete answer.

16/9 = 9 goes into 16 by 1 then (1/8 = 0 with a remainder of 1) then (8 – 1 = 7) = 1.7 with the 7 to infinity
32/9 = 9 goes into 32 by 3 then (3/8 = 0 with a remainder of 3) then (8 – 3 = 5) = 3.5 with the 5 to infinity
64/9 = 9 goes into 64 by 7 then (7/8 = 0 with a remainder of 7) then (8 – 7 = 1) = 7.1 with the 1 to infinity
128/9 = 9 goes into 128 by 14 (14/8 = 1 with a remainder of 6) then (8 – 6 = 2) = 14.2 with the 2 to infinity
256/9 = 9 goes into 256 by 28 (28/8 = 3 with a remainder of 4) then (8 – 4 = 4) = 28.4 with the 4 to infinity
512/9 = 9 goes into 512 by 56 (56/8 = 7 with a remainder of 0) then (8 – 0 = 8) = 56.8 with the 8 to infinity
1024/9 = 9 goes into 1024 by 113 (113/8 = 13 with a remainder of 1) then (8 – 1 = 7) = 113.7 with the 7 to infinity
Etc….

The first method easily works infinitely (simple mathematics) but it’s the second method that isn’t so easy to understand that it also works infinitely. The proof that the second method works to Infinity is the Rule of 1 by 2 by 3. The Rule of 1 by 2 by 3 dictates that if you take 1 and double it to Infinity, the result(s) will not be evenly divisible by 3. This proves that the Rule of 8 by 2 by 9 works to Infinity, because the second method would collapse if the result of any Primary Number (8 x (2 to I)) could be evenly divisible by 9, because the Remainder would then be 0 and there is no way to obtain a .0 answer with the second method and if there is no way for the Primary Number to be evenly divisible by 3, then there is no way it can be evenly divisible by 9.

Another thing to note is the second way to get the second piece of the complete answer, which to do that you simply use the numerology of the original number itself as the second piece of the answer. Which the primer for that is:

Where X = (8 multiplied by (2 to I)) . . . Divide X by 9 to get the whole number portion of the complete answer, then calculate the single digit Base-9 Numerology of X and that answer is the decimal infinity number of the complete answer, which it’s a lot easier to get the answer that way, than the first method but the first method’s purpose isn’t just to do the math the hard way, the first method shows the Base Mathematical Order of the Numbers Puzzle itself, how everything works from within, which proves the perfect equilibrium required for the Numbers Puzzle to work to Infinity, which then also proves the Numbers Puzzle does work to Infinity. Here’s the second way to do the math:

16/9 = 9 goes into 16 by 1 then (1/8 = 0 with a remainder of 1) then (16 = 1 + 6 = 7) = 1.7 with the 7 to infinity
32/9 = 9 goes into 32 by 3 then (3/8 = 0 with a remainder of 3) then (32 = 3 + 2 = 5) = 3.5 with the 5 to infinity
64/9 = 9 goes into 64 by 7 then (7/8 = 0 with a remainder of 7) then (64 = 6 + 4 = 10 = 1 + 0 = 1) = 7.1 with the 1 to infinity
128/9 = 9 goes into 128 by 14 (14/8 = 1 with a remainder of 6) then (128 = 1 + 2 + 8 = 11 = 1 + 1 = 2) = 14.2 with the 2 to infinity
256/9 = 9 goes into 256 by 28 (28/8 = 3 with a remainder of 4) then (256 = 2 + 5 + 6 = 13 = 1 + 3 = 4) = 28.4 with the 4 to infinity
512/9 = 9 goes into 512 by 56 (56/8 = 7 with a remainder of 0) then (512 = 5 + 1 + 2 = 8) = 56.8 with the 8 to infinity
1024/9 = 9 goes into 1024 by 113 (113/8 = 13 with a remainder of 1) then (1024 = 1 + 0 + 2 + 4 = 7) = 113.7 with the 7 to infinity
Etc….

So how do both equations/formulas correspond to the original equation and convert the math differently, to still get the same answer and it works to Infinity?

How do the original numbers work with one another underneath, to create the Perfect Equilibrium for the Numbers Puzzle to work to Infinity on the Surface?

Hint: Look @ the name of the Puzzle:

Rule of 8 by 2 by 9 = Rule of 2³ x 2 x 3²

Sequence Order = 2-3-2-3-2

Three 2’s and Two 3’s, sourcing from the 8 & 9 and using base 10 Open System Numbers (0-thru-10).

Play the Numbers Puzzle to see how the numbers are working underneath, however, the simplicity of the Number Puzzle is the 2^3 never runs into the 3^2 because of the Doubling Factor of the Rule of 1-by-2-by-3, thus, the 8 & 9 never collide and Perfect Order is maintained.

It's the basic math behind Harmony!

Ribbit

 

Yep! That is exactly what binary is. Each digit is (0,1)*2^x
[quote="Toad, post: 235498, member: 1858"
But you can answer the sum of squares with odd numbers only instead and never have to use an even number in the computation.

Odd number summing is easier to understand and predict but even number summing keeps the clutter down and is mathematically organized better and is more flexible in its nature.

Ribbit [/quote]
Back to basic algebra. (X+1)^2 = X^2 +2X +1. In other words (X+1)^2 is 2X+1 larger than X^2. 2X+1 is exactly every odd number. Interesting sequence, but easily explained.

 

I'm kNot meaning to nit-pick but ... .. .

(X+1)^2 is not 2X+1 larger than X^2, it's sum is DIFFERENT by that amount but if 2X + 1 is a negative number then will the outcome be larger or smaller?

Plus, with exactly what you said, you said bad math:

"In other words (X+1)^2 is 2X+1 larger than X^2"

(2X + 1)(X^2) = what you said the answer is and that equates to:

2X^3 + X^2

The 2X+1 comment has to do with Sums not Products but you never clarified either, which is a common mistake made by Closed System Math thinkers. They live by half-ass mathematical generalities and then call them the Whole Truth.

Bullshit!

Ribbit

Ps: Lose the Larger & Smaller thinking, since Everything is Relative to SourCe and SourCe is Relative to Everything.

 

Hey RLM? Since you are willing to talk math, which is difficult to get anyone to dew these days, how many answers are there with every quadratic equation and why?

Ribbit

 

Be aware... He once told us that he was ABOVE the 100th percentile in his class. His math skills are generally from below his belt line.

 

Sure? And you once lied...and once more....and once more.....and once more.....etc.

 

You had a series of consecutive positive numbers. What has that got to do with negative numbers?

BTW, just where did I say anything about "(2X + 1)(X^2)"?

 

The primer werks both ways, positive or negative!

Where did you say something about that? When you used the werd LARGER without clarifying properly.

You assume way too much and assumption does not belong in logic nor mathematics.

Ribbit

 

To be exact as to where you said it:

"In other words (X+1)^2 is 2X+1 larger than X^2."

Those are your exact words and you improperly used the werd LARGER.

Do you kNot know the definition of Ambiguous?

am·big·u·ous
amˈbigyo͞oəs/
adjective
adjective: ambiguous

1.​

(of language) open to more than one interpretation; having a double meaning.

(X+1)^2 is not 2X+1 larger than X^2, the correct way to say what you MEANT to say is:

The Sum of (X+1)^2 is 2X+1 MORE than X^2 by itself.

You used the werd Larger, which was not the correct werd to use, given the werd use used.

Ambiguity in Math is for the stoopid!

Ribbit