The Mathematical Intelligencer

, Volume 40, Issue 1, pp 26–35

# The Mathematics of Taffy Pullers

• Jean-Luc Thiffeault
Article
Taffy is a type of candy made by first heating sugar to a critical temperature, letting the mixture cool on a slab, then repeatedly “pulling”—stretching and folding—the resulting mass. The purpose of pulling is to get air bubbles into the taffy, which gives it a nicer texture. Many devices have been built to assist pulling, and they all consist of a collection of fixed and moving rods, or pins. Figure  1 shows the action of such a taffy puller from an old patent. Observe that the taffy (pictured as a dark mass) is stretched and folded on itself repeatedly. As the rods move, the taffy is caught on the rods and its length is forced to grow exponentially. The effectiveness of a taffy puller is directly proportional to this growth, since more growth implies a more rapid trapping of the air bubbles. Given a pattern of periodic rod motion, regarded as orbits of points in the plane, the mathematical challenge is to compute the growth.

## Notes

### Acknowledgments

Supported by NSF grant CMMI-1233935. The author thanks Alex Flanagan for helping to design and build the 6-rod taffy puller, and Phil Boyland and Eiko Kin for their comments on the manuscript.

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