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The Euler's 8x8 magic square

  • Sam_math
  • | May 13, 2009
  • | 22239 views
  • | 15 comments

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.

Comments


  • 3 years ago

    MCAbbass

    Nice stuff ,actually the set of numbers (natural numbers) also have too much fun imagine if U add to each square (64 squares) in chess board double the the number starting from 1 , at the end U will get this number 1*2^63= 9223,372,036,854,775,808 starting from 1,2,4,8,16,32,64,128 at first row

    second raw    256,512,.........

  • 4 years ago

    Tekoa

    There is one prime number which is even and that is 2.

  • 4 years ago

    lucasp1015

    what the fuck is this pice on crap. I hate fucking black people in the asshole. monkey tits

  • 5 years ago

    zankfrappa

    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.

  • 5 years ago

    1stking123

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

  • 5 years ago

    jonatz_elise

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

  • 5 years ago

    vitali_10

    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...)?!

  • 5 years ago

    ratrosie

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

  • 5 years ago

    Marvin2

    cool

  • 5 years ago

    h777

    cool!

  • 5 years ago

    punkyboy

    thats kind of coolLaughing

  • 5 years ago

    shcp

    thanks!

  • 6 years ago

    RoyalStraightFlush

    Good article. Thanks 4 sharing

  • 6 years ago

    razorblade12

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

  • 6 years ago

    PeterArt

    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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