RE: Mathematical Alchemy (dissecting base 10 numbers via Vortex Based Mathematics, the "digital root" and the nonagon)
5 is spelt "five". I don't understand how you decide what edges to draw in your nonogons. This is also known as addition mod 9. We can consider 9 the same as 0 (mod 9). We can sum two numbers and divide the sum by nine. The remainder is the answer. This is called addition mod 9.
Now the set 0, 1, ... , 8 is said to be a group under this operator because you trivially always get a value from that set when you add mod 9. The nonzero values do not form a group over multiplication mod 9. We have 3*3=0, which is out of the nonzero numbers. Zero can not be considered part of the group under multiplication mod 9 because there is nothing you can multiply by 0 that gives you 1.
In particular 1,4,7 is a group under multiplication mod 9. Now 2,5,8 and 3,6,9 are not. Now multiply by the elements of the group 2x(1,4,7) =(2,8,5) (mod 9) but 3x(1,4,7)=(3,3,3) and 6x(2,5,8) =(3,3,3) (mod 9).
Perhaps in "your" world "five" is spelled "five". Lately for me it is "phi-ve". For the number 5 plays a huge part with the Phi ratio. The pentagram is a great example of this. However I do appreciate your feedback and I do agree with the "mod 9" concept you had mentioned. Marko Rodin himself refers to it as "mod 9". I for one agree again. 0 and 9 are the same essentially I am coming to find in regards to Vortex Based Mathematics. 0 is the singularity, and 9 is the whole, completed, finished process before starting over again in a new cycle, i.e. hence 10 is merely 1 for 1 + 0 = 1, 11 is merely 2 for 1 + 1 = 2, 12 is 3 and so on. Also hopefully I understand your question correctly when you say "how you decide what edges to draw in your nonagons". My answer, I hope indeed correct would be simple. The numbers themselves showed me where to connect the dots on a nonagon to find its geometric constituent themselves. I honestly had no idea what the outcome would be going into this. I have another post where I demonstrate this exact method via placing the doubling PA-ttern of 1-2-4-8-7-5 within a tetraktys and simply added, reduced the sum to their "digital roots" and placed my findings within a box of rows and columns and completed the process until the PA-ttern came around full circle to the beginning again like the ouroboros. Once complete I then placed these numerical PA-tterns with in a nonagon to again find its geometric constituents by simply connecting the dots, the appropriate numbers to be exact. I also have a post where I have done this as well with the "double X" / "dos equis" / Masonic "Square and Compass" symbol or triple merkaba with simply by playing around with our base numbers. PA-tterns within PA-tterns I tell ya of oscillating "solfeggio" number groups that are so orderly and perfect and come around again perfectly full circle like the ouroboros in 9 times that to me it is impossible that this can just be the work of coincidence / chance or what some refer to as merely "Apophenia", the tendency to attribute meaning to perceived connections or patterns between seemingly unrelated things. In which as far as the methods used in this post or my other post I mentioned above is merely not the case I am finding. There is a perfect order / language here. I appreciate your insight brother. I am still learning myself so your input does indeed help me quite a bit to better understand "mod 9" or VBM. So I must say I truly thank you and appreciate that. Namaste brother. :)
I think you misunderstood my question. Let me ask this way:
At the beginning of Part 2, is the paths on the nonogon determined by the tuples 1577761274 and 8741315711?
Yes sir, you are indeed correct. In fact, all four (the two you mentioned pointing upward and the other two pointing downward) tuples in that particular / individual diagram determined the path or line segments that were connected within that particular nonagon. I do apologize for my misunderstanding brother.
I was working on another way of expressing these triangles when I realized there is a kind of mistake in your calculations.
When we are doing subtraction, we may find we subtract a larger number from a smaller number. This gives us a negative value with real values.
I would love to express what I have in neatly typed text but Markdown really sucks for Math. No wonder you used images for all of the notation. Mod 9 subtraction works properly by finding some number that makes the other number sum to 9. So, -8 is 1. -5 is 4.
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Thank you for your input brother. Mistake perhaps, but it was intentional. I would have went the route you wonderfully explained. However by doing the way I did it, where I broke away from using subtraction / negative integers solely, I went and used addition where appropriate. I then noticed / it still reveled to me an obvious PA-ttern. So much so that I went with this route instead rather than using subtraction / negative integers completely. Good find though brother. Great work. :)