Tangentially related: although you're probably suggesting trisecting an edge with origami folds (which is straightforward), the mention of dividing by three using physical methods reminded me of the classic trisecting-an-angle problem, which apparently is also solvable with origami folds [1], even though it isn't solvable with compass and straightedge [2].

[1] https://www.math.lsu.edu/~verrill/origami/trisect/

[2] http://en.wikipedia.org/wiki/Angle_trisection