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The Euler's 8x8 magic square

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Submitted by Sam_math on Wed, 05/13/2009 at 7:01am.

The Euler's 8x8 magic square.

A magic square of order n is an arrangement of n^2 numbers (usually 1, 2, 3...) such that the sum of the numbers in all the rows, columns and big diagonals is a constant.

For example:

An example of a magic square of order 3.

Here the sum of all rows, columns and main diagonals is equal to 15.

This is a very interesting mathematical topic that shows how chess has a big mathematical mistery. Leonard Euler, a very important mathematician, constructed a magic square of order 8, in this square if you put a knight in the 1 you can touch all 64 boxes in consecutive numerical order.

The Euler's 8x8 magic square.

This square solves 2 big problems:

  • To construct a 8x8 magic square.
  • Move a knight in a chessboard visiting all squares 1 and only 1 time.

Conclusion: Math & Chess have many things in common.

» posted in Fun & Trivia
| 2399 reads | 12 comments |
0 votes:
 

Comments:

by zankfrappa - 3 months ago
Virginia United States
Member Since: Nov 2008
Member Points: 2795

I thought for a magic square the diagonals had to add up to the same number as well.  These don't add up like the rows and columns.

by 1stking123 - 4 months ago
Houston United States
Member Since: Jul 2009
Member Points: 15

that is very interesting! i need to show my friends how that works!LaughingLaughingLaughing

by jonatz_elise - 4 months ago
Muntinlupa Philippines
Member Since: Feb 2009
Member Points: 93

That was so cool!! I need to copy that and show it to my classmates!!!

by vitali_10 - 4 months ago
Jerusalem Israel
Member Since: Sep 2007
Member Points: 414

So this idia with the knight probably can be done on every 4nx4n magic square where nэN (n belongs to natural numbers: 1,2,3...)?!

by ratrosie - 5 months ago
Janesville, Wisconsin United States
Member Since: Jun 2009
Member Points: 1

'Mystery' is misspelled, but other than that, great article!

by Marvin2 - 5 months ago
Sydney Australia
Member Since: May 2009
Member Points: 243

cool

by h777 - 5 months ago
Vancouver Canada
Member Since: Nov 2008
Member Points: 8049

cool!

by punkyboy - 6 months ago
Tai Pei Taiwan
Member Since: Jun 2009
Member Points: 345

thats kind of coolLaughing

by shcp - 6 months ago
chicago United States
Member Since: Jan 2009
Member Points: 142

thanks!

by RoyalStraightFlush - 7 months ago
Jakarta Indonesia
Member Since: Apr 2009
Member Points: 507

Good article. Thanks 4 sharing

by razorblade12 - 7 months ago
Herefordshire United Kingdom
Member Since: Dec 2008
Member Points: 804

except 2 as 2 is a prime, even number :P

by PeterArt - 7 months ago
Luijk Belgium
Member Since: Feb 2009
Member Points: 589

nice article if there is anything odd it must be primes.
As by nature, a prime number is an odd number Laughing

Check this link here to checkout chess and primenumbers  !

a sample:

29 (a primenumber) is the maximum number of squares a chess bishop can visit if it is only allowed to visit each square once. (Here, "visit" means that squares passed over in a move are also visited.)

Nice might be 499 too it also deals with the knight on the board much like your version but some different things are going on.

 
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