{"id":27620,"date":"2017-12-29T20:49:20","date_gmt":"2017-12-29T20:49:20","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=27620"},"modified":"2017-12-29T20:49:20","modified_gmt":"2017-12-29T20:49:20","slug":"math-minimum-sum-of-squares","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-minimum-sum-of-squares\/","title":{"rendered":"Math: minimum sum of squares"},"content":{"rendered":"<h1>Tutoring math, you encounter patterns. The tutor brings up one about sums of squares.<\/h1>\n<p>If two whole numbers sum to a constant even one, then their minimum sum of squares will come from each being half. The reason:<\/p>\n<p>Let the numbers sum to 2n, and let the numbers then be n-k and n+k. Then the sum of their squares is<\/p>\n<p>(n-k)<sup>2<\/sup> + (n+k)<sup>2<\/sup><\/p>\n<p>Expanding each square, we get<\/p>\n<p>n<sup>2<\/sup>-2nk+k<sup>2<\/sup> + n<sup>2<\/sup>+2nk+k<sup>2<\/sup>=2n<sup>2<\/sup>+2k<sup>2<\/sup><\/p>\n<p>Therefore, the minimum sum of squares will be achieved when k=0, that is, when n-k=n+k=n.<\/p>\n<p>Source:<\/p>\n<p>Travers, Kenneth J et al. <i>Using Advanced Algebra<\/i>. Toronto: Doubleday Canada Limited, 1977.<\/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>Tutoring math, you encounter patterns. The tutor brings up one about sums of squares. If two whole numbers sum to a constant even one, then their minimum sum of squares will come from each being half. The reason: Let the &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-minimum-sum-of-squares\/\"> <span class=\"screen-reader-text\">Math: minimum sum of squares<\/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":[1107],"class_list":["post-27620","post","type-post","status-publish","format-standard","hentry","category-math","tag-minimum-sum-of-squares"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/27620","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=27620"}],"version-history":[{"count":19,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/27620\/revisions"}],"predecessor-version":[{"id":27639,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/27620\/revisions\/27639"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=27620"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=27620"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=27620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}