Magic Squares

[Racoon]

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

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!

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

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

7 12 1 15
2 14 8 11
17 3 10 5
9 6 16 4

m = 35

[InfiniteNow]

Racoon,

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

[Racoon]

Originally Posted by InfiniteNow

Racoon,

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

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.
I put the Booger in Bloggerer

Magic Square anyone?
Its Mathmagic!

[Buffy]

Originally Posted by InfiniteNow

You're such a serial poster....

The pot calling the kettle black, hmmmmm?

Not above post padding,
Buffy

[pgrmdave]

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

[Racoon]

Originally Posted by Racoon

Math Can Be FUN!

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

This is a cool link!

The Kubera-Kolam used in India

23 28 21
22 24 26
27 20 25

the magic constant = 72

Check out Albrecht Durers Magic Squares too

[InfiniteNow]

Originally Posted by Buffy

The pot calling the kettle black, hmmmmm?

Not above post padding,
Buffy

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

[Turtle]

Originally Posted by Racoon

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

.