{"id":2008,"date":"2023-11-29T10:04:13","date_gmt":"2023-11-29T18:04:13","guid":{"rendered":"https:\/\/theothermath.com\/?p=2008"},"modified":"2023-11-29T10:04:13","modified_gmt":"2023-11-29T18:04:13","slug":"learning-to-count-part-2","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2023\/11\/29\/learning-to-count-part-2\/","title":{"rendered":"Learning to Count &#8211; part 2"},"content":{"rendered":"<p>In this\u00a0<a href=\"https:\/\/theothermath.com\/index.php\/2023\/10\/18\/learning-to-count\/\">previous post<\/a>, I proposed a new way of counting things. If you haven\u2019t already read it, please do so. Otherwise this post won\u2019t make much sense.<\/p>\n<p>In that post I ended with the following problem\u2026<\/p>\n<p><a href=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639.jpeg\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-2009\" src=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639.jpeg\" alt=\"\" width=\"322\" height=\"182\" srcset=\"https:\/\/www.theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639.jpeg 322w, https:\/\/www.theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639-300x170.jpeg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><\/a><\/p>\n<p>How many rectangles are in this 3-by-4 figure?<\/p>\n<p>I promised you an answer to this problem, so here it goes\u2026<\/p>\n<p>For each new rectangle added to the grid, I record the number of NEW rectangles that result. Then I add up all the values.<\/p>\n<p><a href=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639-1.jpeg\"><img loading=\"lazy\" class=\"alignnone wp-image-2010 size-large\" src=\"https:\/\/theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639-1-852x1024.jpeg\" alt=\"\" width=\"750\" height=\"901\" srcset=\"https:\/\/www.theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639-1-852x1024.jpeg 852w, https:\/\/www.theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639-1-250x300.jpeg 250w, https:\/\/www.theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639-1-768x923.jpeg 768w, https:\/\/www.theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639-1-1278x1536.jpeg 1278w, https:\/\/www.theothermath.com\/wp-content\/uploads\/2023\/11\/IMG_0639-1.jpeg 1309w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/a><br \/>\nSo there you have it\u202660 rectangles are in the 3-by-4 grid.<\/p>\n<p>.<\/p>\n<p>.<\/p>\n<p>.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this\u00a0previous post, I proposed a new way of counting things. If you haven\u2019t already read it, please do so. Otherwise this post won\u2019t make much sense. In that post I ended with the following problem\u2026 How many rectangles are in this 3-by-4 figure? I promised you an answer to this problem, so here it [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2015,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[13],"_links":{"self":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/2008"}],"collection":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/comments?post=2008"}],"version-history":[{"count":3,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/2008\/revisions"}],"predecessor-version":[{"id":2013,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/2008\/revisions\/2013"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media\/2015"}],"wp:attachment":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media?parent=2008"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/categories?post=2008"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/tags?post=2008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}