Taffy is a type of candy made by repeated 'pulling' (stretching and
folding) a mass of heated sugar. The purpose of pulling is to get air
bubbles into the taffy, which gives it a nicer texture. Until the late 19th
century, taffy was pulled by hand, an arduous task. The early 20th century
saw an avalanche of new devices to mechanize the process. These devices
have fascinating connections to the topological dynamics of surfaces, in
particular with pseudo-Anosov maps, which are a prototypical chaotic
system. Special algebraic integers such as the Golden ratio and the
lesser-known Silver ratio make an appearance, as well as more exotic
numbers. We examine different designs from a mathematical perspective, and
discuss their efficiency.
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