By George Hart for the Museum of Mathematics


Binder clips are one of the office supplies that aren’t always appreciated for their mathematical possibilities. Where many people see little architectural potential, Zach Abel has been pushing forward the boundaries of binder clip assembly research and offers a number of novel constructions. Here are three. Start with this six-clip exercise in which the clips are positioned along the positive and negative XYZ axes and are each held open by the loops in the handles of their neighbors.

Next, consider this open ball featuring twelve five-pointed stars and twenty hexagons. Its shape derives from a soccer ball, but there are stars instead of pentagons. A total of 120 clips are used to construct this, but sixty of them (at the concave points of the stars) have only one handle.

And for a maximum density spherical packing, check out this sturdy little ball made from 132 clips. The handles of each clip wrap around the bodies of their neighbors to make a regular weaving pattern. At the triangular openings (corresponding to the eight corners of a sphere) the handles lock in a cycle, as a nice touch.

See all of George Hart’s Math Monday columns

Gareth Branwyn

Gareth Branwyn

Gareth Branwyn is a freelance writer and the former Editorial Director of Maker Media. He is the author or editor of over a dozen books on technology, DIY, and geek culture. He is currently a contributor to Boing Boing, Wink Books, and Wink Fun. And he has a new best-of writing collection and “lazy person’s memoir,” called Borg Like Me.

  • Stefanie Mixon Kompathoum

    These will look so pretty with paper-clip chain garlands.

  • Anonymous

    That giant ball is insane. I hope you didn’t suffer any injuries doing that. My fingertips hurt just looking at it.

  • Noah Dennis

    How do you make this???!?!?!!!??

  • Anonymous

    “The eight corners of a sphere” – am I missing something? The eight corners of a box enclosing it?