{"id":2198,"date":"2014-09-03T11:50:36","date_gmt":"2014-09-03T15:50:36","guid":{"rendered":"http:\/\/blog.carlrobitaille.org\/2014\/09\/03\/adding-the-first-n-cubes-in-an-animation\/"},"modified":"2018-11-12T15:14:05","modified_gmt":"2018-11-12T20:14:05","slug":"adding-the-first-n-cubes-in-an-animation","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=2198","title":{"rendered":"Adding the first n cubes, in an animation"},"content":{"rendered":"

Google+ reshared post<\/b><\/p>\n

Adding the first n cubes, in an animation<\/b><\/p>\n

If you add up the first n numbers and square the result, this produces the same answer as adding the first n cubes. This animation by Hydrodium<\/b> on tumblr gives a stunningly good illustration of this identity.<\/p>\n

The graphic shows the case n=5. In this case, the sum of the first 5 natural numbers is 1+2+3+4+5=15, which squares to 15×15=225. On the other hand, the sum of the first n cubes is (1x1x1)+(2x2x2)+(3x3x3)+(4x4x4)+(5x5x5)=1+8+27+64+125, which also adds up to 225. There is nothing special about the number 5 here: an analogous identity holds for any other positive integer, and it can be illustrated by a similar animation.<\/p>\n

At this point, the moderators of the arXiv preprint server would rightly accuse me of \u201csubstantial text overlap\u201d with an earlier post. Yes, I’ve posted about this before (https:\/\/plus.google.com\/101584889282878921052\/posts\/WqimoVTZWL3<\/a>) but this animation does an even better job of showing how everything fits together.<\/p>\n

The animation comes from Hydrodium’s Graphical MathLand<\/i> at http:\/\/hyrodium.tumblr.com\/post\/94237657514\/inspired-by-this-twocubes-post-and-asked-to-make<\/a>
I found it via the blog Visualizing Math<\/i> (http:\/\/visualizingmath.tumblr.com\/<\/a>) which in turn I found via +<\/span>W Younes<\/a><\/span>. There are a lot of very interesting posts on Visualizing Math<\/i>. However, I might be a bit biased in saying that, because I found two of my own recent posts reshared there (with attribution).<\/p>\n

#mathematics<\/a><\/p><\/blockquote>\n

\"\"<\/p>\n

Import\u00e9 de Google+<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Google+ reshared post Adding the first n cubes, in an animation If you add up the first n numbers and square the result, this produces the same answer as adding the first n cubes. This animation by Hydrodium on tumblr … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2198","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/2198","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2198"}],"version-history":[{"count":2,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/2198\/revisions"}],"predecessor-version":[{"id":2292,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/2198\/revisions\/2292"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2198"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2198"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}