{"id":2082,"date":"2016-06-13T09:00:08","date_gmt":"2016-06-13T14:00:08","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=2082"},"modified":"2016-06-13T15:04:23","modified_gmt":"2016-06-13T20:04:23","slug":"world-tessellation-day","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2016\/06\/13\/world-tessellation-day\/","title":{"rendered":"2, 4, 6, 8, It’s Almost Time to Tessellate"},"content":{"rendered":"

This Friday, June 17, is the inaugural World Tessellation Day<\/span><\/a>. I am normally skeptical of attempts to create new holidays, but I am so fond of filling up the plane with shapes that I just can\u2019t help myself.<\/span><\/p>\n

\"No<\/a>

No word on the birds, but bees love to celebrate Tessellation Day. Image copyright Alex Wild. Used with permission.<\/p><\/div>\n

Emily Grosvenor is the tiling enthusiast\u00a0behind the push to make Tessellation Day<\/span><\/a> a thing. She recently successfully crowdfunded Tessalation, a book about a girl named Tessa who sees patterns everywhere. The book will be available for non-backers on June 17, Tessellation Day<\/span><\/a>. (Disclosure: I backed the project on Kickstarter.) The date was chosen because it is the birthday of M. C. Escher, one of the most famous tessellators<\/a>.<\/span><\/p>\n

Luckily, it\u2019s easy to celebrate Tessellation Day. Just tessellate! Appropriately enough, tessellations.org<\/span><\/a> has a tessellation tutorial to get you started. John Golden also has a page of tessellation resources on his blog math hombre<\/span><\/a>, and John Baez has some cool posts about tilings on his AMS blog Visual Insight<\/span><\/a>. Update: Emily Grosvenor also just published a\u00a0list of 23 simple ways to celebrate World Tessellation Day<\/a>.<\/span><\/p>\n

\"A<\/a>

A Penrose tiling. Image: Inductiveload, via WIkimedia Commons. (Public domain.)<\/p><\/div>\n

The easiest shapes to base a tessellation on are equilateral triangles, squares, and regular hexagons<\/span>\u2014<\/span>the regular shapes that fill the plane all by themselves<\/span>\u2014<\/span>but there are lots of other shapes that can form the foundation of your tessellation. I\u2019m particularly fond of pentagons<\/a>, and Laura Taalman has instructions for 3D printing all the tessellating pentagons<\/span><\/a>\u00a0if you\u2019d like to make yourself a desk organizer or other plastic object from irregular pentagons. To break free from the repetition of those tilings, the Penrose tiling<\/span><\/a> is probably everybody\u2019s favorite aperiodic tessellation. You can learn how to knit yourself a Penrose tiling from Woolly Thoughts<\/span><\/a>.<\/span><\/p>\n

One way to make your tessellations a little more exciting is to move them to the hyperbolic plane. Escher of course made a lot of good Euclidean tessellations, but I\u2019m partial to his Circle Limit paintings, which tile the Poincar\u00e9 disc model of the hyperbolic plane. There are good articles about Escher\u2019s use of mathematics and the Circle Limit series in particular by several authors, including Doris Schattschneider<\/span><\/a>, Bill Casselman<\/span><\/a>, and Doug Dunham<\/span><\/a>.<\/span><\/p>\n

\"Image:<\/a>

Image: Pedrita.<\/p><\/div>\n

To elevate your tessellations, you might try venturing into\u00a0the third dimension. It\u2019s not hard to make a 3-dimensional tessellation, or honeycomb, by taking a 2-dimensional tessellation and making it into a prism, but there are other ways of filling 3-space with repeating polyhedra. One of my favorites is the combination of truncated cubes and cubes in this experimental water bottle by Portuguese design firm Pedrita<\/span><\/a>.<\/span><\/p>\n

If you want to\u00a0really get wacky, you can combine hyperbolic geometry and the third dimension and learn about how to visualize hyperbolic honeycombs from Roice Nelson and Henry Segerman<\/span><\/a>.<\/span><\/p>\n

How will you celebrate World Tessellation Day? Share with the hashtag #WorldTessellationDay or #WorldTessDay.<\/span><\/p>\n

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

This Friday, June 17, is the inaugural World Tessellation Day. I am normally skeptical of attempts to create new holidays, but I am so fond of filling up the plane with shapes that I just can\u2019t help myself. Emily Grosvenor … Continue reading →<\/span><\/a><\/p>\n

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