Highly Unlikely Triangles and Other Beaded Mathematics

I first encountered Gwen Fisher’s work at the fiber arts exhibit at 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 beaded group of order 18) in an article I wrote about the fiber arts show. Since then, I’ve been following her blog at her website gwenbeads. She posts about her mathematically inspired beadwork and often includes explanations of the underlying mathematics.

A beaded "highly unlikely triangle." Image copyright Gwen Fisher. Used with permission.

A beaded “highly unlikely triangle.” Image copyright Gwen Fisher. Used with permission.

The bead that caught my eye most recently is the “highly unlikely triangle,” based on the “impossible triangle,” or “Penrose triangle,” that shows up in many M.C. Escher works. Fisher’s triangles 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! She’s also made beaded beads named in honor of mathematicians Harold Coxeter and John Conway.

A beaded snub tetrapentagonal tiling of the hyperbolic plane. Image copyright Gwen Fisher. Used with permission.

A beaded snub tetrapentagonal tiling of the hyperbolic plane. Image copyright Gwen Fisher. Used with permission.

Hyperbolic geometry enthusiasts (like me!) will probably enjoy Fisher’s post about beaded tilings of the hyperbolic plane. Like crochet, 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—and very visually appealing—way. 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.

The Genie Bottle at Burning Man. Image copyright Gwen Fisher. Used with permission.

The Genie Bottle at Burning Man. Image copyright Gwen Fisher. Used with permission.

I’ve just finished helping out with a level 2 Menger sponge build as part of MegaMenger, so I’ve also been interested in Fisher’s posts about the Genie Bottle 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’m tired from just a few days spent folding business cards for our Menger sponge. I’m in awe of how much effort went into the Genie Bottle!

The Genie Bottle goes up in flames at Burning Man. Image copyright Gwen Fisher. Used with permission.

The Genie Bottle goes up in flames. Image copyright Gwen Fisher. Used with permission.

In addition to the blog, Fisher has an etsy shop 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 with fellow mathematician Florence Turnour. All of her sites are interesting if you’re into math, art, and making things!

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1 Response to Highly Unlikely Triangles and Other Beaded Mathematics

  1. Avatar Nick says:

    Did you know that you can use the Penrose triangle effect on other geometrical shapes? A regular polygon for example – Penrose polygon. The visual effect is fascinating.

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