Friday, April 29, 2011

Wonders Of Mathematics - Magic Squares


So one of the books that I really enjoyed recently is the famous Dan Brown's "The Lost Symbol". If you read the book (and you should) you might have noticed that it has many interesting maths references. One of which is hidden in the famous Albrecht Dürer's 1514 engraving Melencolia. It's a very special magic square.

But what are these magic squares? Magic squares are very interesting square arrangements of numbers. The numbers are arranged in such a way, that the sum of all columns, rows and diagonals is equal to the same number.

Magic squares come in different sizes that are called orders, for instance 3x3, 4x4 and so on (it's just a number of rows and columns). As for the sum that is constant for columns, rows and diagonals it's called the magic constant.

 
Image Source

The most simple magic square is of order 3x3 (it's easy to see that 2x2 squares are not possible). But how do you construct such a magic square, without relying to guess work? There are various rules, which can help you construct the square faster, however some guess work is still essential.

So when stumbled across these magic squares, I decide it would be fun to found a 3x3 magic square without any help. It's quite fun, well at least much more fun than sudoku, so I encourage you to try it.

Thanks for reading. Next time we're gonna look at all possible 3x3 magic squares and at the mysterious Melancolia engraving.

5 comments:

Sinead said...

I am confused.

"The numbers are arranged in such a way, that the sum of all columns, rows and diagonals is equal to the same number."

Why would a 2x2 not work?

1 1
1 1 ... the sums of both rows = 2, columns = 2 and diagonal = 2

Same with every other 2x2 where all the numbers are equal?

Am I adding it up wrong?

Sinead said...

Oooo *googled* they have to be distinct numbers.. never mind! Lol!

silentbob14 said...

Yeah that was what I thouth at first too.

Krishna said...

Magic Squares first appeared in one of the temples of India in Madhya Pradesh. I think its related to Vedic Maths or something. Alex Bello's book - Alex in Numberland also talks about it.

silentbob14 said...

Thanks, sounds interesting. I'll check out the book. Cheers

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