{"id":821,"date":"2014-10-27T08:00:50","date_gmt":"2014-10-27T13:00:50","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=821"},"modified":"2014-10-26T23:30:27","modified_gmt":"2014-10-27T04:30:27","slug":"highly-unlikely-triangles-gwenbeads","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2014\/10\/27\/highly-unlikely-triangles-gwenbeads\/","title":{"rendered":"Highly Unlikely Triangles and Other Beaded Mathematics"},"content":{"rendered":"

I first encountered Gwen Fisher\u2019s work at the fiber arts exhibit\u00a0at the 2014 Joint Mathematics Meetings in Baltimore. Fisher has a Ph.D. in math education and is an accomplished mathematical artist who specializes in beading. I featured one of her pieces<\/a>\u00a0(a beaded group of order 18<\/a>) in an article<\/a> I wrote about the fiber arts show. Since then, I\u2019ve been following her blog at her website gwenbeads<\/a>. She posts about her mathematically inspired beadwork and often includes explanations of the underlying mathematics.<\/p>\n

\"A<\/a>

A beaded “highly unlikely triangle.” Image copyright Gwen Fisher. Used with permission.<\/p><\/div>\n

The bead that caught my eye most recently is the \u201chighly unlikely triangle<\/a>,\u201d based on the \u201cimpossible triangle,\u201d or \u201cPenrose triangle<\/a>,\u201d that shows up in many M.C. Escher works. Fisher’s\u00a0triangles are not actually impossible, but they do seem to twist around in an unlikely way. A link from that post led me to Borromean linked beaded beads and a highly unlikely hexagon<\/a>! She\u2019s also made beaded beads<\/a> named in honor of mathematicians Harold Coxeter<\/a> and John Conway<\/a>.<\/p>\n

\"A<\/a>

A beaded snub tetrapentagonal tiling of the hyperbolic plane. Image copyright Gwen Fisher. Used with permission.<\/p><\/div>\n

Hyperbolic geometry enthusiasts (like me!) will probably enjoy Fisher’s post about beaded tilings of the hyperbolic plane<\/a>. Like crochet<\/a>, it seems that beading can allow for a slight increase in area around vertices that distributes the negative curvature of the hyperbolic plane in an even\u2014and very visually appealing\u2014way. Fisher has beaded several different tilings of the hyperbolic plane: the {4,5} tiling (5 squares around every vertex) and the rhombitetrahexagonal and snub tetrapentagonal tilings, both of which use multiple shapes. I think the prettiest one is the snub tetrapentagonal tiling made of pink pentagons, yellow squares, and green triangles shown above.<\/p>\n

\"The<\/a>

The Genie Bottle at Burning Man. Image copyright Gwen Fisher. Used with permission.<\/p><\/div>\n

I\u2019ve just finished helping out with a level 2 Menger sponge build as part of MegaMenger<\/a>, so I\u2019ve also been interested in Fisher\u2019s posts about the Genie Bottle<\/a> she and her group Struggletent built at Burning Man this year. It was a giant, furnished, climbable sculpture. It was also ephemeral, spectacularly going up in flames at the end of the event. I\u2019m tired from just a few days spent folding business cards for our Menger sponge. I\u2019m in awe of how much effort went into the Genie Bottle!<\/p>\n

\"The<\/a>

The Genie Bottle goes up in flames. Image copyright Gwen Fisher. Used with permission.<\/p><\/div>\n

In addition to the blog, Fisher has an etsy shop<\/a> where she sells tutorials for many of her designs as well as beads, hats, jewelry, and other items she makes. She also runs a business called beAd Infinitum<\/a> with fellow mathematician Florence Turnour. All of her sites are interesting if you\u2019re into math, art, and making things!<\/p>\n

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I first encountered Gwen Fisher\u2019s work at the fiber arts exhibit\u00a0at the 2014 Joint Mathematics Meetings in Baltimore. Fisher has a Ph.D. in math education and is an accomplished mathematical artist who specializes in beading. I featured one of her … Continue reading →<\/span><\/a><\/p>\n

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