{"id":133,"date":"2019-02-26T10:00:52","date_gmt":"2019-02-26T15:00:52","guid":{"rendered":"https:\/\/annie.mathematicalthinking.org\/?p=133"},"modified":"2019-02-26T20:26:45","modified_gmt":"2019-02-27T01:26:45","slug":"conway-tangles","status":"publish","type":"post","link":"https:\/\/annie.mathematicalthinking.org\/index.php\/2019\/02\/26\/conway-tangles\/","title":{"rendered":"Learning More about Conway&#8217;s Rational Tangles"},"content":{"rendered":"<p>I just led the <a href=\"http:\/\/pamtc.org\/\" target=\"_blank\" rel=\"noopener\">Philly Area Math Teachers&#8217; Circle<\/a> and did a version of John Conway&#8217;s Rational Tangles.\u00a0 I don&#8217;t claim to know everything about them by a long shot, but I put this together in case some of the participants want to explore more beyond what we covered in math circle.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_3040.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-140 size-thumbnail\" src=\"https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_3040-150x150.jpg\" alt=\"\" width=\"150\" height=\"150\" srcset=\"https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_3040-150x150.jpg 150w, https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_3040-100x100.jpg 100w\" sizes=\"(max-width: 150px) 100vw, 150px\" \/><\/a>\u00a0<a href=\"https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_5378-copy.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-142 size-thumbnail\" src=\"https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_5378-copy-150x150.jpg\" alt=\"\" width=\"150\" height=\"150\" srcset=\"https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_5378-copy-150x150.jpg 150w, https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_5378-copy-100x100.jpg 100w\" sizes=\"(max-width: 150px) 100vw, 150px\" \/><\/a><a href=\"https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_3038.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-141 size-thumbnail\" src=\"https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_3038-150x150.jpg\" alt=\"\" width=\"150\" height=\"150\" srcset=\"https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_3038-150x150.jpg 150w, https:\/\/annie.mathematicalthinking.org\/wp-content\/uploads\/2019\/02\/IMG_3038-100x100.jpg 100w\" sizes=\"(max-width: 150px) 100vw, 150px\" \/><\/a><\/p>\n<p>My interest in this started when my husband traveled with me to the Northwest Math Conference in Whistler in 2018. He&#8217;s a retired high school math teacher, so I told him to go to Fawn&#8217;s session because she would make him do math.\u00a0 They did this activity in her session, so I decided I&#8217;d do it when I was leading our local math circle this February.<\/p>\n<p><a href=\"http:\/\/fawnnguyen.com\/students-embroiled-conways-rational-tangles\/\" target=\"_blank\" rel=\"noopener\">Fawn Nguyen: Students Embroiled in Conway&#8217;s Rational Tangles<\/a>\u00a0[Blog post]. Fawn learned about this activity in a math circle.\u00a0 Here she reports out on trying it with her students.\u00a0 Be sure to watch the charming video at the end!<\/p>\n<p><a href=\"http:\/\/www.geometer.org\/mathcircles\/tangle.pdf\" target=\"_blank\" rel=\"noopener\">Tom Davis: Conway&#8217;s Rational Tangles<\/a> [PDF]. Everyone seems to point to this or at least mention it, so I figured I better too.<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/playlist?list=PLRa5gIXimPcafOko8uJ9EGMATxZNlZsM4\" target=\"_blank\" rel=\"noopener\">Tom Davis: Conway&#8217;s Rational Tangles<\/a> [Video]. Don&#8217;t want to read the PDF above? Head on over to YouTube and watch all 21 videos in the playlist of Tom leading this activity in a math circle.<\/p>\n<p><a href=\"https:\/\/www.mathteacherscircle.org\/assets\/session-materials\/JTantonRationalTangles.pdf\" target=\"_blank\" rel=\"noopener\">James Tanton: Understanding Rational Tangles<\/a>\u00a0[PDF].\u00a0 Want to dig into the math of this?\u00a0 So did James, and he wrote about it.<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/playlist?list=PLL0ATV5XYF8BfT8CmmzKnfTlf3V9hQgj9\" target=\"_blank\" rel=\"noopener\">Matthew Salomone: Math 596: Topics in Algebra and Knots<\/a> [Video]. Ever wondered what an non-Abelian group is? Check out these support materials for Matthew&#8217;s course. (Hint: non-Abelian comes up in the third video and you will totally understand it.)\u00a0 Oh, and it also explains, with visual aids, a bunch of the math about rational tangles.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I just led the Philly Area Math Teachers&#8217; Circle and did a version of John Conway&#8217;s Rational Tangles.\u00a0 I don&#8217;t claim to know everything about them by a long shot, but I put this together in case some of the participants want to explore more beyond what we covered in math circle. \u00a0 My interest &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/annie.mathematicalthinking.org\/index.php\/2019\/02\/26\/conway-tangles\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Learning More about Conway&#8217;s Rational Tangles&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":143,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/posts\/133"}],"collection":[{"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/comments?post=133"}],"version-history":[{"count":4,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/posts\/133\/revisions"}],"predecessor-version":[{"id":144,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/posts\/133\/revisions\/144"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/media\/143"}],"wp:attachment":[{"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/media?parent=133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/categories?post=133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/annie.mathematicalthinking.org\/index.php\/wp-json\/wp\/v2\/tags?post=133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}