Preprint Open Access

Generating Pythagorean Triples, Patterns, and Magic Squares

Inder J. Taneja

MARC21 XML Export

<?xml version='1.0' encoding='UTF-8'?>
<record xmlns="">
  <datafield tag="041" ind1=" " ind2=" ">
    <subfield code="a">eng</subfield>
  <datafield tag="653" ind1=" " ind2=" ">
    <subfield code="a">Pythagorean triples, Pandigital patterns, Palindromic-type patterns, Magic Squares</subfield>
  <controlfield tag="005">20200120174053.0</controlfield>
  <controlfield tag="001">2544555</controlfield>
  <datafield tag="856" ind1="4" ind2=" ">
    <subfield code="s">561815</subfield>
    <subfield code="z">md5:3e4483891615a3f1b6031697abde2223</subfield>
    <subfield code="u"></subfield>
  <datafield tag="542" ind1=" " ind2=" ">
    <subfield code="l">open</subfield>
  <datafield tag="260" ind1=" " ind2=" ">
    <subfield code="c">2019-01-20</subfield>
  <datafield tag="909" ind1="C" ind2="O">
    <subfield code="p">openaire</subfield>
    <subfield code="o"></subfield>
  <datafield tag="100" ind1=" " ind2=" ">
    <subfield code="u">Formarly,  Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil</subfield>
    <subfield code="a">Inder J. Taneja</subfield>
  <datafield tag="245" ind1=" " ind2=" ">
    <subfield code="a">Generating Pythagorean Triples, Patterns, and Magic Squares</subfield>
  <datafield tag="540" ind1=" " ind2=" ">
    <subfield code="u"></subfield>
    <subfield code="a">Creative Commons Attribution 4.0 International</subfield>
  <datafield tag="650" ind1="1" ind2="7">
    <subfield code="a">cc-by</subfield>
    <subfield code="2"></subfield>
  <datafield tag="520" ind1=" " ind2=" ">
    <subfield code="a">&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;</subfield>
  <datafield tag="773" ind1=" " ind2=" ">
    <subfield code="n">doi</subfield>
    <subfield code="i">isVersionOf</subfield>
    <subfield code="a">10.5281/zenodo.2544554</subfield>
  <datafield tag="024" ind1=" " ind2=" ">
    <subfield code="a">10.5281/zenodo.2544555</subfield>
    <subfield code="2">doi</subfield>
  <datafield tag="980" ind1=" " ind2=" ">
    <subfield code="a">publication</subfield>
    <subfield code="b">preprint</subfield>
All versions This version
Views 493494
Downloads 236236
Data volume 132.6 MB132.6 MB
Unique views 432433
Unique downloads 205205


Cite as