{"id":571,"date":"2012-11-20T18:59:30","date_gmt":"2012-11-21T01:59:30","guid":{"rendered":"http:\/\/www.wayupnorth.ca\/blog\/?p=571"},"modified":"2012-11-20T18:59:30","modified_gmt":"2012-11-21T01:59:30","slug":"tiling-the-non-euclidian-plane","status":"publish","type":"post","link":"https:\/\/www.wayupnorth.ca\/blog\/2012\/11\/20\/tiling-the-non-euclidian-plane\/","title":{"rendered":"Tiling the non-Euclidian Plane"},"content":{"rendered":"

I’ve always been intrigued by the soccer ball with its hexagons and pentagons, and with the mind-bending artwork of M.C. Escher.\u00a0 The fact that the two were mathematically related totally escaped me until recently.\u00a0 I do OK with basic arithmetic, but quickly get lost when they start mixing non-Roman script with the variables.\u00a0 So I approached the VizMath<\/a> MOOC with an expectation that I was going to be totally lost.\u00a0 I am lost, but wander in amazement at the genius and the beauty.\u00a0 I am not particularly worried about finding my way.<\/p>\n

Daina Taimina’s crocheted creations<\/a> are a good example.\u00a0 While not even pretending to understand how these might represent (or fail to represent) the shape of the universe, they drew me in, made me believe I might copy them, if never understand them.\u00a0 It wasn’t until she showed us the rough approximations of her work in hexagons though, that I found my inspiration to act – and blog.<\/p>\n

\"\"

positive vs. negative curvature<\/p><\/div>\n

In an attempt to share some of the wonder with my ABE math students, I created a sheet of pentagons, hexagons, and heptagons to cut out and tape together.\u00a0 There are enough polygons on one sheet to make a complete circle of both curved and negatively curved (hyperbolic) planes.\u00a0 Extension of the planes, either to a complete sphere or complete insanity will require additional sheets, and probably collaborative effort.<\/p>\n

\"download<\/a>Click the image at the left to download a PDF version of my worksheet.<\/p>\n

(And yes, I do know there are extra hexagons. I couldn’t bring myself to waste the white space when it’s so easy to crowd them.\u00a0 Just be thankful my childhood training in frugality wasn’t so overpowering that I had to tile them.\u00a0 I was tempted…)<\/p>\n

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

I’ve always been intrigued by the soccer ball with its hexagons and pentagons, and with the mind-bending artwork of M.C. Escher.\u00a0 The fact that the two were mathematically related totally escaped me until recently.\u00a0 I do OK with basic arithmetic, … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[1],"tags":[36,48,47,49],"class_list":["post-571","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-vizmath","tag-bamboozled-and-bedazzled","tag-hyperbolic-plane","tag-scissors-and-tape"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p1xsA3-9d","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/posts\/571","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/comments?post=571"}],"version-history":[{"count":16,"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/posts\/571\/revisions"}],"predecessor-version":[{"id":604,"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/posts\/571\/revisions\/604"}],"wp:attachment":[{"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/media?parent=571"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/categories?post=571"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayupnorth.ca\/blog\/wp-json\/wp\/v2\/tags?post=571"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}