{"id":11898,"date":"2013-04-10T22:50:58","date_gmt":"2013-04-11T03:50:58","guid":{"rendered":"http:\/\/blog.kenperlin.com\/?p=11898"},"modified":"2013-04-10T23:12:48","modified_gmt":"2013-04-11T04:12:48","slug":"hexagonal","status":"publish","type":"post","link":"http:\/\/blog.kenperlin.com\/?p=11898","title":{"rendered":"Pyramid power"},"content":{"rendered":"<p>This week I learned a wonderful thing:  If you assemble spheres to make hexagons of different sizes (up to N spheres on a side), and then stack up those hexagons to make a pyramid, you get exactly the same number of spheres as if you made a cube with N spheres on a side.<\/p>\n<p>I was so delighted by this that I wrote a little computer program to visualize it.<\/p>\n<p>Below you can see the cases where the hexagons contain up to two, three or four spheres on a side, respectively.  Next to each picture you see spheres arranged into a cube.  In each case (and in fact in every possible case), the number of spheres is the same on the left and on the right.<\/p>\n<p>How cool is that!<\/p>\n<p><center><\/p>\n<table>\n<tr>\n<td valign=center>\n<img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2013\/04\/p2.png\" alt=\"p2\" title=\"p2\" width=\"200\" height=\"140\" class=\"aligncenter size-full wp-image-11899\" \/><\/td>\n<td valign=center>\n<img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2013\/04\/c2.png\" alt=\"c2\" title=\"c2\" width=\"200\" height=\"150\" class=\"aligncenter size-full wp-image-11900\" \/><\/td>\n<\/tr>\n<tr>\n<td valign=center>\n<img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2013\/04\/p31.png\" alt=\"p31\" title=\"p31\" width=\"200\" height=\"150\" class=\"aligncenter size-full wp-image-11917\" \/><\/td>\n<td valign=center>\n<img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2013\/04\/c3.png\" alt=\"c3\" title=\"c3\" width=\"200\" height=\"150\" class=\"aligncenter size-full wp-image-11902\" \/><\/td>\n<\/tr>\n<tr>\n<td valign=center>\n<img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2013\/04\/p4.png\" alt=\"p4\" title=\"p4\" width=\"200\" height=\"150\" class=\"aligncenter size-full wp-image-11903\" \/><\/td>\n<td valign=center>\n<img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2013\/04\/c4.png\" alt=\"c4\" title=\"c4\" width=\"200\" height=\"150\" class=\"aligncenter size-full wp-image-11904\" \/><\/td>\n<\/tr>\n<\/table>\n<p><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This week I learned a wonderful thing: If you assemble spheres to make hexagons of different sizes (up to N spheres on a side), and then stack up those hexagons to make a pyramid, you get exactly the same number of spheres as if you made a cube with N spheres on a side. I &hellip; <a href=\"http:\/\/blog.kenperlin.com\/?p=11898\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Pyramid power&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/11898"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11898"}],"version-history":[{"count":16,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/11898\/revisions"}],"predecessor-version":[{"id":11921,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/11898\/revisions\/11921"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11898"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11898"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}