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Creative Magic Squares: Area Representations

Inder J. Taneja


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    <subfield code="a">&lt;p&gt;It is well known that every magic square can be written as &lt;strong&gt;perfect square sum&lt;/strong&gt; of entries. It is always possible with odd number entries starting from 1. In case of odd order magic squares we can also write with &lt;strong&gt;consecutive natural number&lt;/strong&gt;&amp;nbsp;entries. Still, it is unknown whether it is possible to even order magic squares. In case of odd order magic squares, still we can write them with &lt;strong&gt;minimum perfect square&lt;/strong&gt;&amp;nbsp;sum of entries. Based on this idea of &lt;strong&gt;perfect square sum&lt;/strong&gt; of entries, we have written a magic square representing areas. This is done 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 more that one way. It is due to the fact that we can always write magic squares as &lt;strong&gt;normal&lt;/strong&gt;, &lt;strong&gt;bordered&lt;/strong&gt;&amp;nbsp;and &lt;strong&gt;block-bordered&lt;/strong&gt;&amp;nbsp;ways.&lt;/p&gt;</subfield>
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