strange pattern

[josh_0]

Hi, I noticed a strange pattern going on in numbers 369.
Now before you crucified me as a tesla fan, conspirator or anything like that.
i just want to show you what i actually meant.
when multiply 3 linearly it will always give the same pattern like so,
3*1 = 3
3*2 = 6
3*3 = 9
3*4 = 12 -> 1+2 = 3
3*5 = 15 -> 1+5 = 6
3*6 = 18 -> 1+8 = 9
etc..
when i get to the 39 in that series its still continue when i add the digits to the base 10 system
39 -> 3+9 = 12 - > 1+2 = 3
42 -> 4+2 = 6
45 -> 4+5 = 9
the pattern of 369 always appear, most likely endlessly.
same method apply on 6 give me the 639 pattern and 9 give me the 999.
I would be happy for an explanation and sorry for my English

 

[Deleted member 4993]

Hi, I noticed a strange pattern going on in numbers 369.
Now before you crucified me as a tesla fan, conspirator or anything like that.
i just want to show you what i actually meant.
when multiply 3 linearly it will always give the same pattern like so,
3*1 = 3
3*2 = 6
3*3 = 9
3*4 = 12 -> 1+2 = 3
3*5 = 15 -> 1+5 = 6
3*6 = 18 -> 1+8 = 9
etc..
when i get to the 39 in that series its still continue when i add the digits to the base 10 system
39 -> 3+9 = 12 - > 1+2 = 3
42 -> 4+2 = 6
45 -> 4+5 = 9
the pattern of 369 always appear, most likely endlessly.
same method apply on 6 give me the 639 pattern and 9 give me the 999.
I would be happy for an explanation and sorry for my English

There is a "theorem" in number theory that states that:

When the digits of a number divisible by 3 are added (repeatedly till the output is a number with one digit), the result will be 3, 6 or 9.

also

When the digits of a number divisible by 9 are added (repeatedly till the output is a number with one digit), the result will be 9.

 

[josh_0]

i aware of the 3 divisibility rule, but the sequence is what interesting.
unfortunately the subject is shrouded in conspiracies, and I can not find a single article that gives a more realistic explanation.
the answer you provide is good but partial, there is still no absolute explanation for the phenomenon that it is always in the same infinite order of 369.
If questions like this are not to your liking, I will understand and just research it myself.

 

[HallsofIvy]

That's called "casting out nines".

Casting out nines - Wikipedia

en.wikipedia.org

 

[Deleted member 4993]

i aware of the 3 divisibility rule, but the sequence is what interesting. Unfortunately the subject is shrouded in conspiracies, and I can not find a single article that gives a more realistic explanation. The answer you provide is good but partial, there is still no absolute explanation for the phenomenon that it is always in the same infinite order of 369.
If questions like this are not to your liking, I will understand and just research it myself.

3, 6 and 9 are "consecutive" numbers divisible by 3. Thus the sequence 369 does not surprise me. It would have been surprising if the sequence was 396.

 

[Dr.Peterson]

Hi, I noticed a strange pattern going on in numbers 369.
Now before you crucified me as a tesla fan, conspirator or anything like that.
i just want to show you what i actually meant.
when multiply 3 linearly it will always give the same pattern like so,
3*1 = 3
3*2 = 6
3*3 = 9
3*4 = 12 -> 1+2 = 3
3*5 = 15 -> 1+5 = 6
3*6 = 18 -> 1+8 = 9
etc..
when i get to the 39 in that series its still continue when i add the digits to the base 10 system
39 -> 3+9 = 12 - > 1+2 = 3
42 -> 4+2 = 6
45 -> 4+5 = 9
the pattern of 369 always appear, most likely endlessly.
same method apply on 6 give me the 639 pattern and 9 give me the 999.
I would be happy for an explanation and sorry for my English

The thing you should be studying is "modular arithmetic".

Your addition of digits, called "casting out nines", results in a single digit that is the remainder after dividing by 9 (except that you get 9 instead of 0). If you do this with successive numbers (i.e. applying it to 1, 2, 3, ...), the results are 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, ... . This is called counting "modulo 9". If you do it with successive multiples of 3 (counting by 3's), the results will count by 3's modulo 9: 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, ..., which is what you found.

If you do this with multiples of 6, which is "congruent to -3 modulo 9", you count backward by 3's: 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, ... . And if you do it with multiples of 9, you always get 9; in effect, you are "counting by zeros".

None of this is the least bit surprising to someone who knows a little about modular arithmetic. So definitely look that up and explore. I think you'll find it interesting.

unfortunately the subject is shrouded in conspiracies, and I can not find a single article that gives a more realistic explanation.

I can't imagine who's supposed to be conspiring!

 

[josh_0]

The thing you should be studying is "modular arithmetic".

Your addition of digits, called "casting out nines", results in a single digit that is the remainder after dividing by 9 (except that you get 9 instead of 0). If you do this with successive numbers (i.e. applying it to 1, 2, 3, ...), the results are 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, ... . This is called counting "modulo 9". If you do it with successive multiples of 3 (counting by 3's), the results will count by 3's modulo 9: 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, ..., which is what you found.

If you do this with multiples of 6, which is "congruent to -3 modulo 9", you count backward by 3's: 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, ... . And if you do it with multiples of 9, you always get 9; in effect, you are "counting by zeros".

None of this is the least bit surprising to someone who knows a little about modular arithmetic. So definitely look that up and explore. I think you'll find it interesting.



I can't imagine who's supposed to be conspiring!

a cynical response at the end of the explanation, but I understand your point
thanks.

That's called "casting out nines".

Casting out nines - Wikipedia

en.wikipedia.org

3, 6 and 9 are "consecutive" numbers divisible by 3. Thus the sequence 369 does not surprise me. It would have surprising if the sequence was 396.

thanks to you all guys you may close this thread if you wish.

 

[Dr.Peterson]

a cynical response at the end of the explanation, but I understand your point
thanks.

I was expressing curiosity about how this could be "shrouded in conspiracies". I'm guessing that you don't mean literal claims that someone conspired to make this happen. I don't see how that's "cynical".

 

[josh_0]

I was expressing curiosity about how this could be "shrouded in conspiracies". I'm guessing that you don't mean literal claims that someone conspired to make this happen. I don't see how that's "cynical".

everything about Tesla unfortunately borders on conspiracies, not because his claims are untrue. But mainly because it is human nature to do so. a lot of people who do not understand the essence of his research. and turn to conspiracy theorists to find answers.
see "Tesla 369" entry and you will find countless blogs and unsubstantiated research on Google