{"id":1925,"date":"2016-04-04T14:11:31","date_gmt":"2016-04-04T19:11:31","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=1925"},"modified":"2016-04-04T14:11:31","modified_gmt":"2016-04-04T19:11:31","slug":"how-to-celebrate-square-root-day","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2016\/04\/04\/how-to-celebrate-square-root-day\/","title":{"rendered":"How to Celebrate Square Root Day"},"content":{"rendered":"

Apparently today, 4\/4\/16, is Square Root Day.<\/span><\/a> (I supposed we could also have celebrated 4\/2 to have a long Square Root Weekend.) How should a math enthusiast celebrate this holiday, which won’t come again until May\u00a02025?<\/span><\/p>\n

\"8

8 squares arranged in a curve of pursuit. Image: Evelyn Lamb.<\/p><\/div>\n

Of course, one option is to be a curmudgeon. As a curmudgeon myself<\/span><\/a>, I heartily support you in this endeavor, and Michael Lemonick of Scientific American<\/span><\/a> does as well. If, however, you are not as cold and dead inside<\/span><\/a> as he and I are, I\u2019ve got\u00a0some lovely square facts and activities for you. <\/span><\/p>\n

I\u2019ve got to lead off with one of the coolest things I learned last month, courtesy of Matt Baker<\/span><\/a>.<\/span><\/p>\n

\n

Let n be a positive integer.\u00a0 <\/span>It is easy to see that a square can be dissected into n triangles of equal area if n is even (Exercise).\u00a0 <\/span>What if n is odd?\u00a0 <\/span>If you play with the question for a bit, you probably won\u2019t be surprised to learn that in this case it\u2019s impossible.\u00a0 <\/span>But you may be surprised to learn that this result was not proved until 1970, that the proof involved p-adic numbers, and that no proof is known which does not make use of p-adic numbers!<\/span><\/p>\n<\/blockquote>\n

I find it shocking and delightful that a fairly simple question about plane geometry requires p-adics to solve. If, like me<\/span><\/a>, you\u2019re a bit uncomfortable with p-adics, cut-the-knot math has a p-adic page<\/span><\/a> where you can learn about these strange completions of the rationals.<\/span><\/p>\n

A more traditional way of celebrating might be to ponder the wonderful Pythagorean theorem.\u00a0Cut-the-knot has more proofs of it than you can shake a stick at<\/a>, and I’m still enchanted by Albert Einstein’s elegant proof, which\u00a0Steven Strogatz wrote about last November<\/a>.<\/p>\n

Arts and crafts have many opportunities for square-making. One of my favorite square-centric designs is a curve of pursuit: out of tilted squares, curves seem to appear. The excellent mathematical knitting site Woolly Thoughts has some information about how to knit curves of pursuit<\/span><\/a>. A few years ago, my grandparents celebrated their 82<\/sup>-th anniversary, so I made them a tablecloth with 8 squares arranged in a curve of pursuit. You can see it in the picture at the top of this post or read about it here<\/span><\/a>.<\/span><\/p>\n

Last year, Math Munch shared a project called SquareRoots by John Sims<\/span><\/a>. Inspired by the quilts of Gee\u2019s Bend<\/a>, he made mathematical quilts based on the base 3 digits of pi. And for more mathematical quilts, check out the\u00a0gorgeous ones on Elaine Ellison\u2019s website<\/span><\/a>.<\/span><\/p>\n

If you want to take your square explorations up a dimension or two (because who has time to wait until 4\/3\/64 or 4\/4\/(2)256?), Numberphile has a lovely video<\/span><\/a> about higher-dimensional Platonic solids, including the hypercube, and Mike Lawler has been making hypercubes with his kids<\/span><\/a>.<\/span><\/p>\n

It\u2019s baseball opening day today as well (\u221a \u221a \u221a for the home team<\/a>!), and Patrick Vennebush of Math Jokes for Mathy Folks has combined the two topics for a guess-the-graph game<\/span><\/a>.<\/span><\/p>\n

How will you be square today?<\/span><\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

Apparently today, 4\/4\/16, is Square Root Day. (I supposed we could also have celebrated 4\/2 to have a long Square Root Weekend.) How should a math enthusiast celebrate this holiday, which won’t come again until May\u00a02025? Of course, one option … Continue reading →<\/span><\/a><\/p>\n

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