# Magic Squares

1. Jan 12, 2004

### pallidin

Greetings,

I suppose all of us have at one time or another been fascinated by "magic squares"
My question is: has the relationship of numbers in a magic square been found to be useful in the mathematical sciences in any advanced analytical work? Or is is just a mathematical curiousity?

2. Jan 12, 2004

### pallidin

Follow-up question:

Has a 3-D model of a magic square been developed?

3. Jan 13, 2004

### KLscilevothma

4. Jan 19, 2004

### oen_maclaude

try this problem

suppose you have 9 boxes of chocolates. the first box contains 1 piece, the 2nd 2, the 3rd 3 and so on up to 9th box contains 9. the problem now is how to distribute these boxes to 3 people such that these people would have equal number of chocolates without opening the boxes?

this is quite a classical example yet this may be solved using the numbers in the magic square.

5. Jan 19, 2004

### recon

First Person: 2, 7, 6

Second Person: 1, 9, 5

Third Person: 3, 4, 8

6. Jan 19, 2004

### KLscilevothma

Put the boxes in three rows:

2 9 4
7 5 3
6 1 8

They can take either the (2,9,4), (7,5,3), (6,1,8) combination or (2,7,6), (9,5,1), (4,3,8) combination.

7. Jan 19, 2004

### oen_maclaude

Put the boxes in three rows:
2 9 4
7 5 3
6 1 8

taking into account the table of values above would be the entries in the 3x3 magic square.

8. Jan 25, 2004

### metacristi

There is a special class of magic squares labeled Latin,Greek and Greco-Latin (obtained from a superposition of two Latin squares or a Greek and a Latin square) which are often used in the applied statistics for the design of scientific experiments.A Latin square is a (nxn) square where are arranged Latin letters (and possible some extra signs if n is greater than the number of latin letters) so that they occur once in each row and once in each column.They were widely studied by Euler more than 250 years ago who conjectured that there cannot exist Greco-Latin squares of the order [(4k+2)x(4k+2)] due to the fact that he couldn't find a (6x6) Greco-Latin square (he did not proved that a 6x6 square cannot exist however).In our days his conjecture was disproved,only (2x2) and (6x6) Greco-Latin magic squares do not exist.

Euler made another conjecture in his writings namely that it is not likely to find an experimental application for magic squares in general.However we was wrong again for no later than 150 years later Greco Latin squares proved very useful in the statistical design of experiments in agriculture.The idea is that instead of testing all combinations possible (very difficult sometimes in practice) it is much economical to choose a relevant sample from which can be obtained results relevant for the whole combinations possible.The variables involved in the process studied are arranged in the form of a Greco-Latin square representing the relvant sample for all combinations possible.If additional parameters are needed into the study they are simply introduced by merging the initial Greco-Latin square with the Latin squares formed with the new parameters into a new Greco Latin square representing the relavant sample which to be tested practically.

Last edited: Jan 25, 2004
9. Jul 9, 2007

### Qaiser Raza

Hello there!
Yes ! I have developed 3D models of Magic Squares.