Math Monday: Grocery Geometry

by Glen Whitney

MoMath colleague Dave Masunaga and I were chewing on some of the tasty macadamia nuts, while chewing on some interesting problems that may show up in the Museum of Mathematics this December, when we realized that the pleasant and unusual geometry of the packaging of these nuts provided excellent fodder for some spur-of-the moment mathematical makery. A couple packs of binder clips and not too many minutes later led to the first of this week’s offerings, the Siernutski Tetrahedron:If only Dave had been hungrier when shopping and bought another box, we could have extended this to order three. But the conveniently flexible nature of the packaging does lead to a number of other interesting, dynamic structures, such as this ring of Tumbling Nutrahedra, which rotates about itself in the manner of a smoke ring:(You can build a paper model of this structure using this template.) Inspired by these constructions, a quick trip proved that the grocery store is a fertile hunting ground for the raw material for momathematical creations. For example, some octahedral cookie packs lent themselves to this Truncookied Cube. Note that all three flavors meet at every triangular opening, providing a pleasingly uniform mathematicogustatory experience:However, this construction seemed as though it might be a bit dry — a situation quickly rectified by the introduction of antipodal pairs of six different flavors of tea, to produce the TruncaTea-ed Biscubottihedron:Enterprising readers are invited to send images of their own grocery geometry; we’d love to see what you’re up to.

This article first appeared on Make: Online, May 21, 2012.

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