Preprint Open Access

Generating Pythagorean Triples, Patterns, and Magic Squares

Inder J. Taneja


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  <identifier identifierType="DOI">10.5281/zenodo.2544555</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>Generating Pythagorean Triples, Patterns, and Magic Squares</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2019</publicationYear>
  <subjects>
    <subject>Pythagorean triples, Pandigital patterns, Palindromic-type patterns, Magic Squares</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2019-01-20</date>
  </dates>
  <language>en</language>
  <resourceType resourceTypeGeneral="Preprint"/>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/2544555</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.2544554</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;This &amp;nbsp;paper brings simplified and symmetric procedure to generate &lt;strong&gt;Pythagorean triples&lt;/strong&gt;. &amp;nbsp;These triples are obtained in different procedures. First procedure is given in three blocks. The second procedure is the extension of first procedure, but in little different way. These triples are applied to generate &lt;strong&gt;perfect square sums magic squares&lt;/strong&gt;&amp;nbsp;of &lt;strong&gt;consecutive odd numbers&lt;/strong&gt;, and &amp;nbsp;&lt;strong&gt;patterned Pythagorean triples&lt;/strong&gt;. The patterned Pythagorean triples are obtained in two different way. One is a general way, and the second procedure give us &lt;strong&gt;Palindromic-Type Pandigital Pythagorean Triples&lt;/strong&gt;&amp;nbsp;in two different forms. As examples, the magic squares of orders 3 to 20 are given. The sum of entries of magic squares always give a &lt;strong&gt;perfect square&lt;/strong&gt; resulting in a &lt;strong&gt;Pythagorean triple&lt;/strong&gt;.&lt;/p&gt;</description>
  </descriptions>
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