Preprint Open Access

Creative Magic Squares: Area Representations With Fraction Numbers Entries

Inder J. Taneja

It is well known that every magic square can be written as perfect square sum of entries. It is always possible with consecutive odd numbers entries starting from 1. In case of odd order magic squares we can also write with consecutive natural numbers entries. In case of even order magic squares it is possible with consecutive fraction numbers entries. Still we can have minimum perfect square sum of entries in two different ways, i.e., one with consecutive natural numbers for odd order magic squares and  secondly with consecutive fraction numbers entries for even order magic squares. Based on this idea of perfect square sum of entries, magic square are written as area-representations of each number resulting always in perfect square sum of entries. The work is for the magic squares of orders 3 to 11. In the case of magic squares of orders 10 and 11 the images are not very clear, as there are a lot of numbers. To have a clear idea, the magic squares are also written in numbers. In all the cases, the area representations are given in more that one way. It is due to the fact that we can always write magic squares as normal, bordered and block-bordered ways. This work is revised version of author's previous work. This work brings more results with \textbf{fraction numbers} entries. In future the work shall be extended for higher order magic squares.

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