By George Hart for the Museum of Mathematics

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Here is a wide variety of mathematical beadwork structures by Horibe Kazunori.

beads 0 Math Monday: Mathematical Beadwork

Looking closely at one example, you can see how the surface curvature depends on the structure. Generally, six-sided cycles correspond to an infinite tessellation of hexagons, which makes a flat plane or can be rolled into a cylinder. But in the places where positive curvature (a spherical region) is desired, some pentagons are used instead of hexagons. And in places where negative curvature (a saddle-shaped region) is desired, some heptagons are used instead of hexagons. With this knowledge, the bead designer can control the surface outcome.

beads 1 Math Monday: Mathematical Beadwork

Horibe gives detailed instructions for making a beaded buckyball here. (It is in Japanese, but the pictures explain it all.)

More:
See all of George Hart’s Math Monday columns

Gareth Branwyn

Gareth Branwyn is a freelancer writer and the former Editorial Director of Maker Media. He is the author or editor of a dozen books on technology, DIY, and geek culture, including the first book about the web (Mosaic Quick Tour) and the Absolute Beginner’s Guide to Building Robots. He is currently working on a best-of collection of his writing, called Borg Like Me.


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