{"id":1109,"date":"2018-04-09T08:55:26","date_gmt":"2018-04-09T14:55:26","guid":{"rendered":"http:\/\/blog.inkofpark.com\/?p=1109"},"modified":"2025-10-21T19:00:14","modified_gmt":"2025-10-22T01:00:14","slug":"hexagonal-blanket-dimensions","status":"publish","type":"post","link":"https:\/\/www.inkofpark.com\/?p=1109","title":{"rendered":"Hexagonal Blanket Dimensions"},"content":{"rendered":"<p><a href=\"http:\/\/www.inkofpark.com\/wp-content\/uploads\/2018\/03\/hex_geometry.png\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"244\" title=\"hex_geometry\" style=\"display: inline; background-image: none;\" alt=\"hex_geometry\" src=\"http:\/\/www.inkofpark.com\/wp-content\/uploads\/2018\/03\/hex_geometry_thumb.png\" border=\"0\"><\/a><\/p>\n<p>Look at the right-most figure in diagram. The small triangle defines the all the major dimensions of the hexagon. Assuming the user measures the edge-to-edge dimension $c$, he or she can calculate the rest of the measurements. A simple right-triangle expression gives the relationship between $s\/2$ and $c\/2$, and is readily solved for $s$ in terms of $c$,<br \/>\n$$ \\frac{s}{2} = \\frac{c}{2}\\tan\\left(30\u00b0\\right) $$<br \/>\n$$&nbsp; s = c\\tan\\left(30\u00b0\\right) = c\\frac{\\sqrt{3}}{3}. $$<\/p>\n<p>Similarly, the Pythagorean formula gives the relationship between $c$ and the two other dimensions,<br \/>\n$$&nbsp; d = \\sqrt{ c^2 + s^2} = \\frac{2c}{\\sqrt{3}}.$$<\/p>\n<p>Simplifying this equation by substituting for $s$ into the previous equation and simplifying produces<br \/>\n$$&nbsp; \\text{long pitch} = s + \\frac{d-s}{2} = \\frac{s+d}{2}&nbsp; = \\frac{\\sqrt{3}}{2}c \\approx 0.87c. $$<\/p>\n<p>A blanket $n$ hexagons by $m$ hexagons will be approximately<br \/>\n$$<br \/>\n0.87c\\,n \\times m\\,c, $$<br \/>\nwhere the $m$ and $n$ dimensions are as shown in the next figure.\n<\/p>\n<p><a href=\"http:\/\/www.inkofpark.com\/wp-content\/uploads\/2018\/03\/hex_packing.png\"><img loading=\"lazy\" decoding=\"async\" width=\"508\" height=\"357\" title=\"hex_packing\" style=\"display: inline; background-image: none;\" alt=\"hex_packing\" src=\"http:\/\/www.inkofpark.com\/wp-content\/uploads\/2018\/03\/hex_packing_thumb.png\" border=\"0\"><\/a><\/p>\n<p>If a blanket will be wider at the ends, as shown in the figure, then $n$ will be odd. The total number of hexagons will then be<br \/>\n$$ \\text{number of hexagons} = m \\frac{n+1}{2} + (m-1)\\frac{n-1}{2}. $$<\/p>\n<p>In the example there are $(n+1)\/2=5$ tall columns and $(n-1)\/2=4$ short columns. So there are 6\u00d75=30 hexagons in tall columns and (6-1)\u00d74=20 hexagons in the short columns, or 50 hexagons overall. Using equation for blanket size and assuming $c=10$ inches, the approximate dimensions of the finished blanket are 9\u00d710\u00d70.87 by 6\u00d710, or 78.3 by 60 inches.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Look at the right-most figure in diagram. The small triangle defines the all the major dimensions of the hexagon. Assuming the user measures the edge-to-edge dimension $c$, he or she can calculate the rest of the measurements. A simple right-triangle expression gives the relationship between $s\/2$ and $c\/2$, and is readily solved for $s$ in [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":1107,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-1109","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-making"],"_links":{"self":[{"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/posts\/1109","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1109"}],"version-history":[{"count":6,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/posts\/1109\/revisions"}],"predecessor-version":[{"id":1239,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/posts\/1109\/revisions\/1239"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/media\/1107"}],"wp:attachment":[{"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1109"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1109"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}