Math Is Fun Forum

fdjohan

Member

Registered: 2021-05-26

Posts: 3

Magic Triangle

Hi all, I am not an expert in math. But I found something interesting. Please see the images.

Question:
- What do you call these number connections?
- Has someone ever found this triangle connection before?

Thanks in advance.
Ferry

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Magic Triangle

hi Ferry,

Welcome to the forum.

Great diagrams.  But what are we supposed to be noticing?  Are you able to post some more examples?

LATER EDIT: As my morning has gone on I've given this more thought. Can I make my own example?

Just choosing numbers at random, the answer was no.  So then I thought I'd try some algebra.

In place of the top numbers, 9 and 2 I put N ad M.  In place of the bottom addition number (4) I put x.  Then I developed the triangle according to what I think are the rules.

So bottom left I calculated N - x - 1 and M + x + 1.

Bottom right I had N - x - 2 and M = x + 2

Across the bottom I formed equations by requiring that x is the add number.

N - x - 1 + x = M + x + 2
and
N - x - 2 + x = M + x + 1

Fortunately these both simplify to the same equation:

N = M + x + 3

So now I'm in a position to construct my own example.  I want N, M and x all to be whole numbers under 10 so I chose M = 1 and x = 3.

That requires N = 1 + 3 + 3 = 7 and the numbers at the vertices are 71, 35 and 62. And that's as far as I've progressed.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

fdjohan

Member

Registered: 2021-05-26

Posts: 3

Re: Magic Triangle

You are a genius Bob. No. I can't make other samples.  I thought it's just regular three numbers. But when I learned about the connections, they are beautifully composed. But one thing I notice (my sample). In Cross-connection, The combination number of the differentials is 211. The prime no. 47 is 211.
Also, The prime no: 92 is 479 and 47 - 9 = 38 ----again we find 92-47-38.
Thank you for working on it. That is amazing.
Ferry

Last edited by fdjohan (2021-05-27 17:49:44)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Magic Triangle

Hi Ferry,

With that equation there are quite a few solutions.  So it's not so remarkable to find one with other interesting properties.  When I get a moment I'll see if I can add a second constraint based on what I'll call the cross-differences.  I've just got to find a pencil, some paper and some time.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Magic Triangle

Left hand cross differences:

N - M - x -1  and  N -x - 1 -M
These are the same.  And if I substitute for N

M + x + 3 - x - 1 - M = 2 for all N, M and x.

In the same way you can prove that the right hand cross differences are equal to 1 and the bottom ones are also 1.

So 211 is the result for every set of N, M and x.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

fdjohan

Member

Registered: 2021-05-26

Posts: 3

Re: Magic Triangle

Thanks Bob. Only I don't understand complicated math. My humble brain can only understand, 92,47, and 38 are really remarkable numbers. Not only they are interlinked with each other, but such numbers also can be produced from the Prime Number. It's a challenge for the mathematician to produce something like it.
Thank you for your responses.
Ferry.

Last edited by fdjohan (2021-05-29 01:04:56)