{"id":13806,"date":"2016-01-07T21:18:13","date_gmt":"2016-01-07T21:18:13","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=13806"},"modified":"2016-01-07T21:18:13","modified_gmt":"2016-01-07T21:18:13","slug":"math-pythagorean-triples","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-pythagorean-triples\/","title":{"rendered":"Math:  Pythagorean triples"},"content":{"rendered":"<h1>The tutor gives a few integer solutions to a<sup>2<\/sup>+b<sup>2<\/sup>=c<sup>2<\/sup>.<\/h1>\n<p>All-integer solutions to a<sup>2<\/sup>+b<sup>2<\/sup>=c<sup>2<\/sup> are called Pythagorean triples.  They are comparativeley rare.  Here are three sets I know:<\/p>\n<p>3,4,5<\/p>\n<p>5,12,13<\/p>\n<p>8,15,17<\/p>\n<p>From the sets above, infinitely more can be generated: multiplying all three of a set by the same number gives another one.  Therefore, some additional Pythagorean triples are<\/p>\n<p>6,8,10 and 9,12,15 (based on 3,4,5)<\/p>\n<p>10,24,26 (based on 5,12,13)<\/p>\n<p>80,150,170 (based on 8,15,17)<\/p>\n<p>I&#8217;ll be talking more about Pythagorean triples.<\/p>\n<p>Source:<\/p>\n<p>Dudley, Underwood.  <em>Elementary Number Theory<\/em>, 2nd Ed.  New York:  W H Freeman<br \/>&nbsp;&nbsp; and Company, 1978.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor gives a few integer solutions to a2+b2=c2. All-integer solutions to a2+b2=c2 are called Pythagorean triples. They are comparativeley rare. Here are three sets I know: 3,4,5 5,12,13 8,15,17 From the sets above, infinitely more can be generated: multiplying &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-pythagorean-triples\/\"> <span class=\"screen-reader-text\">Math:  Pythagorean triples<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[1329,1327,1328],"class_list":["post-13806","post","type-post","status-publish","format-standard","hentry","category-math","tag-abc","tag-number-theory","tag-pythagorean-triples"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13806","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=13806"}],"version-history":[{"count":11,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13806\/revisions"}],"predecessor-version":[{"id":13817,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13806\/revisions\/13817"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=13806"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=13806"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=13806"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}