There is a newer version of this record available.

Preprint Open Access

# Creative Magic Squares: Area Representations

Inder J. Taneja

### DataCite XML Export

<?xml version='1.0' encoding='utf-8'?>
<resource xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://datacite.org/schema/kernel-4" xsi:schemaLocation="http://datacite.org/schema/kernel-4 http://schema.datacite.org/meta/kernel-4.1/metadata.xsd">
<identifier identifierType="DOI">10.5281/zenodo.5009224</identifier>
<creators>
<creator>
<creatorName>Inder J. Taneja</creatorName>
<affiliation>Formarly, Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil</affiliation>
</creator>
</creators>
<titles>
<title>Creative Magic Squares: Area Representations</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2021</publicationYear>
<subjects>
<subject>Magic Squares, Area representations, pefect square sums</subject>
</subjects>
<dates>
<date dateType="Issued">2021-06-22</date>
</dates>
<language>en</language>
<resourceType resourceTypeGeneral="Preprint"/>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/5009224</alternateIdentifier>
</alternateIdentifiers>
<relatedIdentifiers>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.5009223</relatedIdentifier>
</relatedIdentifiers>
<rightsList>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
</rightsList>
<descriptions>
<description descriptionType="Abstract">&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;</description>
</descriptions>
</resource>

137
91
views