10. Ring Sets

When I first started looking at vortex math one of the first things I did was to take Marko Rodin’s symbol and add the numbers that are next to each other and write them in a new ring.

First lets take a brief look at Marko’s symbol

00rodinssymbol

There are a few things going on in the middle but for now we are only looking at the numbers around the edge, these numbers are our 1 times table and by putting them in a circle we capture the finite female pattern of our infinite 1 times table.

I wanted to know how these numbers related to their neighbours. So lets start with our one times table.

01

Now lets add another ring.

set02

Now lets add the numbers that are next to each other and place the result in between them on the next ring out.

set03

Now this I found interesting, if we start at the 9 at the bottom and go clockwise we have the female pattern of our 2 times table created from the 1 times table in the first ring.

Lets continue to the next ring using the same process.

set04

Again starting with the 9 and go clockwise the female pattern of the 4 times table is created all by its self.
I was getting really excited by this and was expecting the 5 times table to be in the next ring, lets see

set05

Well I was wrong and it was the female pattern of the 8 times table, I was still very excited.
lets continue.

set06

This produced the female 7 times table and that just left the female 5 times table and if we continue to the next ring it is created.

set07

Now we could just keep adding rings but what we find is that the next ring out will just repeat the first ring. so in 6 rings we have a complete ring set. Each you can spin around each ring forever adding 1 on the first ring, 2 on the second ring, 4 on the third ring, 8 on the fourth ring, 7 on the fifth ring  or 5 on the sixth ring.

Lets have a look at this ring set in a little more depth.
The first thing I noticed is all the 3s all the 6s and all the 9s all lined up.

set08

Next lets look at how the other family member groups arrange themselves.

set09

We have three rings that start from the 9 at the top and three rings that start from the 9 at the bottom.
We find that the rings that start from the top are the 1,4 and 7 times table and the 2, 5  and 8 are upside down

set10

This is the ring set for all our multiplications we have our 1, 2, 4, 8, 7 and 5 times table contained in each ring and this pattern is a very key pattern that we will be looking at in depth later, but for now notice that all the times table for the 9 family group hidden.

To find the 3 times table we are only going to use the rings of the 3 family group, so that would be the 1 4 and 7 times table or the first, third and fifth rings.

set11

We are starting from 9 and working clockwise just like we did in each ring and we can use the same method to find the 6 times table

set12

It is interesting to overlay the two patterns and we have something very similar to some sacred geometry.

set13

Remember this pattern would keep going if we were to keep adding rings.
That just leaves the 9 times table and that is found vertically down the centre.

So there we have our first ring set and it is complete we cant add anything to it without repeating what is already there. I was very excited.

set08

We shall be making more ring sets as we look at more number sequences.

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