"Leibniz even suggested that the catenary could be used as a device for calculating logarithms, and "analog" logarithmic table of sorts. "This may help," he said, "since on long trips one may lose his table of logarithms." Was he suggesting that one should carry a chain in his pocket as a backup logarithmic table?"
from e: The Story of a Number by Eli Maor
Leibniz was writing in 1690, and was talking of the relationship between the curve described by a hanging chain (a catenary) and the natural logarithmic base e - a useful but irrational number that presumably can be derived from a catenary curve (the book does not go into detail).
I love this idea of a tangible device that connects person with abstract mathematics, without the distance and encoding/decoding of pen and paper, or a computer, or even a calculator, although these are similarly portable as well. The beaty of these examples, the abacus, a hanging chain, vernier calipers, sextants, slide rules, is that simply through their mechnics, they can help the user understand a mathematical concept, or see first hand how a mathematical concept is relevant to a tangible, physical system. There must be more examples... I mourn the increasing use of the electronic computer at the cost of purely mechanical computers.