Magic Squares

[Racoon]

Seems the more I learn, the less I realize I know! :eek:

 

Doing a little bit of history, I came across the Legend of Lo Shu, who presented himself to the emporer with a "Magic Square" on his Turtle Shell!

 

And when reading the popular thread "Strange Numbers", this seemed to resonate as well.

 

A Magic Square is a curious arrangement of numbers also known as a sacred square.

 

heres an example:

 

4 9 2

3 5 7

8 1 6

 

It all adds up to fifteen no matter what direction you add up the numbers!

Its pretty neat, and kinda' fun! :D

 

M(n) = n^3 + n / 2

 

Magic squares of order n= 3,4,5.....

create magic constants of 15, 34, 65, 111, 175, 260,.....

 

What do you think?

Here are a couple links to get started.

Math Can Be FUN! :)

 

http://en.wikipedia.org/wiki/Magic_Square

[Racoon]

Although the Application is more for Fun, Magic Squares do lead into work of group theories, lattices, Latin squares, matrices, determinants, partitions, and congruence :eek:

 

heres a good that might stimulate some Neurons:

 

http://www.reference.com/browse/wiki/Magic_square

[Racoon]

heres a special 4 x 4 Magic Square, from the above link.

seems 13 had to be dropped :phones:

 

7 12 1 15

2 14 8 11

17 3 10 5

9 6 16 4

 

m = 35 :evil:

[InfiniteNow]

Racoon,

 

You're such a serial poster. Have you considered being a bloggerer? :hihi:

[Racoon]

Racoon,

 

You're such a serial poster. Have you considered being a bloggerer? :hihi:

 

This is all I do Online. Except for some research

I'll burn out after a while, and take a Va-Kay.

 

It must be all the cool people. :cool: :hihi:

I put the Booger in Bloggerer :hihi:

 

Magic Square anyone?

Its Mathmagic! :)

[Buffy]

You're such a serial poster....

The pot calling the kettle black, hmmmmm?

 

Not above post padding, :hihi:

Buffy

[pgrmdave]

There's never any post padding here! Only serious scientific inquiry :hihi:

[Racoon]

Math Can Be FUN! :cool:

 

http://en.wikipedia.org/wiki/Magic_Square

 

This is a cool link!

 

The Kubera-Kolam used in India :hihi:

 

23 28 21

22 24 26

27 20 25

 

the magic constant = 72

 

Check out Albrecht Durers Magic Squares too :)

[InfiniteNow]

You're such a serial poster....

The pot calling the kettle black, hmmmmm?

 

Not above post padding, :)

Buffy

 

I post in parellel, thank you very much. Hmmppff! :hihi:

[Turtle]

Although the Application is more for Fun,...

 

More for fun now perhaps, but once more for metaphysics. Beginning with the lowest number in the square, put a pen down & draw a continuous line from it to each sequential number [1 to 2 to 3...etc.]; you now have a 'magic path' or 'magic line'. The form is then graven on amulets or written as part of the ritual of casting spells. Every planet has an associate magic square to go with all the other symbols & qualities of astrology, numerology, etceterology.

Ben Franklin, loyal Mason that he was, created some never before known magic squares, & they continue to provide a recreational bit to many people. The maths you mention simply model certain aspects of magic squares; that is to say magic squares don't provide solutions per se.

Albrecht Durers famous square incorporates the date he painted it if I remember.

Now even though it is the case that I have shown in the Katabatak thread how to map one-to-one square matrices onto triangular matrices, the magic of magic squares in this isomorphism is not preserved. It goes away, & at best one has psuedo-magic triangles.

This is squarely enough about that

.:computer:

[pgrmdave]

According to this site:

http://www.delphiforfun.org/whatsnew/WhatsNew_Jan2003.htm

Dürer's square contained 15|14 in the bottom, because he created it in 1514

[Jay-qu]

There's never any post padding here! Only serious scientific inquiry :)

whos post padding..

 

:eek2:

[Turtle]

One of the books I owned on Black Magic printed one of the magic squares with an error. How many spelss have gone wrong over that one!? (I think it was the 9x9 sqaure).

Here's something to try with them. Find their inverse so to speak. Take the 3x3 for example & replace each number with its difference from 10. Try the same with other but take the difference from 1 more than the total number of cells.

That is all I have to say at this time about that.:eek2: :)

[Racoon]

According to this site:

http://www.delphiforfun.org/whatsnew/WhatsNew_Jan2003.htm

That site looks kinda' lame.

not too much info. but that 15/14 fact is pretty cool.

I try and search a bit before I post any link

[Racoon]

*bump

 

Generalizations

Extra constraints

Certain extra restrictions can be imposed on magical squares. If not only the main diagonals but also the broken diagonals sum to the magic constant, the result is a panmagic square. If raising each number to certain powers yields another magic square, the result is a bimagic, a trimagic, or, in general, a multimagic square.

Different constraints

Sometimes the rules for magic squares are relaxed, so that only the rows and columns but not necessarily the diagonals sum to the magic constant. In heterosquares and antimagic squares, the 2n + 2 sums must all be different.

Other operations

Instead of adding the numbers in each row, column and diagonal, one can apply some other operation. For example, a multiplicative magic square has a constant product of numbers.

Image:MultiplicativeMagicSquare-Order3.png Image:MultiplicativeMagicSquare-Order4.png

M = 216 M = 6720