Well... since I created a thread on a math and philosophy site about this but people there seem not so interested in it, I found out this site and hope for some interesting discussion

Here's a 3x3 magic square.



So everyone knows each line sums up to 15, but there's probably much more about it.

1x3=3
3x3=9
9x3=27
27x3=81
81x3=243 and so on
Notice the last digit. It's 1>3>9>7>1>3>...
Look at the square to check how 1>3>9>7>1>3 goes. It's a clockwise cycle.

Now let's see how the number 2 works.
2x2=4
4x2=8
8x2=16
16x2=32
32x2=64
So 2>4>8>6>2 and it's a anti-clockwise cycle.

It's not only limited to these two numbers but actually it works with every number.
I will sum it up here

for odd number,
1 is a 360 degree mutiplier
3 is a 90 degree mutiplier
9 is a 180 degree mutiplier
7 is a 270 degree mutiplier

for even number,
2 is a 270 degree mutiplier
4 is a 180 degree mutiplier
8 is a 90 degree mutiplier
6 is a 360 degree multiplier

so 1,6; 2,7; 3,8; 4,9 are pairs

And what about the number 5?
It's the centre. Every number is neutralized by the number 5 when mutiplying it.
Odd number will get 5 and even number will get 10.

And what about the hidden number 10?
Look at all opposite numbers.
1+9=10
2+8=10
3+7=10
4+6=10

Let me remind you that we are doing the calculation with a 10 based system.
So the hidden number 10 actually reflects the square is running with the 10based.


It's all I have discovered.
Maybe we can learn something new about number through the magic square.


Here's a 5x5 magic sqaure. Let's try it yourself.


Hint: The system is not 10 based anymore


So guys, what's your thought

This is pretty stupid. So there are some sequences the magic square appears to adhere to. Now what?

Beauty.

my first thought....

So besides maybe framing it and hanging it on your wall, is there any use for this "magic square?"

It's good to see somebody doing some recreational mathematics.

Imo magic square is a number system which gives a new direction to how numbers can be put and work together.


The 60 digit cycle of Fibonacci sequence

1,1,2,3,5,8,3,1,4,5,9,4,3,7,10
7,7,4,1,5,6,1,7,8,5,3,8,1,9,10
9,9,8,7,5,2,7,9,6,5,1,6,7,3,10
3,3,6,9,5,4,9,3,2,5,7,2,9,1,10

You can see these 4 rows follow the magic sqaure cycle.

It's hard to say if there's any use with it. Well, IMO it's a number system. It can be used in many ways.
But honestly, I'm not able to link the abstract idea behind the system to any practical stuff

I was the one who discovered the super secret way to spell "BOOBIES" on a calculator. Sadly, none of my professors were impressed. Yet.

f#&$#& iPhone....

can't do it....$&##%((

Unfortunately, I don't think these things are "new." But I also don't know what you mean by a "number system."

I don't know how to reconcile your first sentence with your third sentence.

* It's hard to say if there's any use.
* It can be used in many ways.

Which is it?

Sometimes, there are just patterns that have no meaning. Given that you've got two posts so far on this forum, I'm slightly inclined to make a guess that you're going to end up giving some sort of numerology post.

For reference:

http://forums.philosophyforums.com/t...ics-71152.html

How about creating a magic square where all entries are squares themselves (n_ij^2). That is unsolved for some small cases like 3x3,4x4 i think i read before.

http://mathworld.wolfram.com/MagicSquare.html
http://en.wikipedia.org/wiki/Magic_square

http://math.stackexchange.com/questi...are-of-squares

http://www.multimagie.com/Search.pdf

Technology doesn't always move society forward.

Sorry for my harsh post. I was put off by the following:
-This pattern holds for this magic square. Does it necessarily hold for any magic square of any size? Insights on why?
- The 'hidden' 10. This is a 3x3 magic square. The magic number - center square will always be sum of all opposite numbers. This is not something special, e.g. because we use a 10-based system (how do you define an n-based system?).
That there is no practical relevance to what was found was not really what bugged me.

I already said you could try it with the 5x5. I will show you anyway.



1x5=5
5x5=25
25x5=125=4(26) 21
125x5=625=24(26) 1

this system is a 26based because the sum of all opposite numbers is 26.

Hello Dynamic,
You figured out very closed to the ancient Oriental metaphysic system. Have you heart of He Tu and Luoshu? The pair that you got 1,6,27,38,49 and 5,10 in the He Tu. The magic square already discovered by the ancient that you to create Luoshu and the Baqua, which create the basic system for accurate forecasting