{"id":4017,"date":"2025-05-02T19:34:36","date_gmt":"2025-05-02T19:34:36","guid":{"rendered":"https:\/\/redfrontdoor.org\/blog\/?p=4017"},"modified":"2025-05-02T19:34:36","modified_gmt":"2025-05-02T19:34:36","slug":"juggling-ball-pyramids-and-a-christmas-song","status":"publish","type":"post","link":"https:\/\/redfrontdoor.org\/blog\/?p=4017","title":{"rendered":"Juggling-ball pyramids and a Christmas song"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">One of many identities within Pascal&#8217;s triangle goes, I recently learnt, by the name of <em>The Hockey-Stick Identity<\/em>, or sometimes <em>The Christmas Stocking Identity<\/em>.  It tied together two situations which on the face of it are not at all related \u2014 a juggling show, and the song <em>The Twelve Days of Christmas<\/em>.  It&#8217;s now May, so this post is not as seasonal as it might have been, but nonetheless here it is.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"640\" src=\"https:\/\/redfrontdoor.org\/blog\/wp-content\/uploads\/2025\/05\/hockey-stick-two-pyramids.jpg\" alt=\"Juggler Domenyk La Terra standing next to two pyramids of juggling balls, each pyramid atop a pillar.\" class=\"wp-image-4016\" style=\"width:476px;height:auto\" srcset=\"https:\/\/redfrontdoor.org\/blog\/wp-content\/uploads\/2025\/05\/hockey-stick-two-pyramids.jpg 640w, https:\/\/redfrontdoor.org\/blog\/wp-content\/uploads\/2025\/05\/hockey-stick-two-pyramids-300x300.jpg 300w, https:\/\/redfrontdoor.org\/blog\/wp-content\/uploads\/2025\/05\/hockey-stick-two-pyramids-150x150.jpg 150w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><figcaption class=\"wp-element-caption\">Image: Domenyk La Terra<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\">The write-up<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/bennorth.github.io\/hockey-stick-identity-examples\/\">The full write-up is hosted on GitHub here<\/a> and includes an exciting interactive dragging sliding thing for the Twelve Days of Christmas!<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Colophon<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The <a href=\"https:\/\/github.com\/bennorth\/hockey-stick-identity-examples\/\">source for the above-linked write-up<\/a> is a mixture of markdown, raw HTML, and raw JavaScript.  I used <a href=\"https:\/\/pandoc.org\/\">pandoc<\/a> to convert the markdown to HTML, with styling provided by <a href=\"https:\/\/github.com\/bgw\/pan-am\/\">Benjamin Woodruff&#8217;s Pan Am<\/a> (under <a href=\"https:\/\/github.com\/bgw\/pan-am\/blob\/master\/LICENSE\">a permissive licence<\/a>) and tweaked slightly.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Explaining how a relationship within Pascal&#8217;s triangle explains both The Twelve Days of Christmas and a pleasing feature of a juggling performance.<\/p>\n","protected":false},"author":2,"featured_media":4016,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4017","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","comments-off"],"_links":{"self":[{"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4017","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4017"}],"version-history":[{"count":4,"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4017\/revisions"}],"predecessor-version":[{"id":4021,"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4017\/revisions\/4021"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=\/wp\/v2\/media\/4016"}],"wp:attachment":[{"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/redfrontdoor.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}