By Willis AIREY, With B&W illus.
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Extra resources for A learner in China: a life of Rewi Alley
6(c), (d) the FAT algorithm was executed on every other suitable vertex along the edge of the tape so that, in (c), the resulting figure, or its flipped version, could be woven together in a more symmetric way and, in (d), the excess could be folded neatly around the points. It is now natural to ask: (1) Can we use the same general approach used for folding a convex 7-gon to fold a convex N -gon with N odd, at least for certain specified values of N ? If so, can we always prove that the actual angles on the tape really converge to the putative angle we originally sought?
Our instructions seem to be, on the whole, quite comprehensible to most readers. However, there are two basic types of error that people seem prone to make in carrying out our instructions. Material error In doing mathematics, it is absurd to specify the quality of paper on which the mathematics should be done. However, when we describe to you how to make mathematical models, we must insist that the choice of material is not arbitrary. Instructions for making models that are easily constructed using gummed mailing tape are unlikely to be effective if a strip of paper taken from an exercise book is used instead.
5, would have to satisfy the equation 2x1 + π3 + = π, from which it follows that x1 = π3 − 2 . In the same way we can see that the new angle, x2 , created by the upward fold line, shown in frame 7, would have to satisfy the equation 2x2 + x1 = 2x2 + π3 − 2 = π, from which it follows that x2 = π3 + 22 . Continuing in this way we find that xk = π3 + (−1)k 2k . This tells us that every time we make a correct fold the error is cut in half and changes sign. So after 10 correct fold lines the error must be smaller than 1024 !
A learner in China: a life of Rewi Alley by Willis AIREY, With B&W illus.