This problem is identical to the design of the heel of a sock. Since this is traditionally women’s work it is not considered to be inherently mathematical while the industrial problem is.
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Consider the problem of lagging a pipe for a chemical factory so that the
material does not bunch up at the inside of the angle or stretch out at the outside of the
angle. Compound the problem by requiring the pipe to be able to occasionally open up to
about 180 degrees. This problem is identical to the design of the heel of a sock. Since this is traditionally women’s work it is not considered to be inherently mathematical while the industrial problem is. |
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Here is a mathematical formulation of the solution to this problem using a method from traditional women’s work, knitting.
| Turn heel as
follows:— 1st row—K.12 [14, 16], sl.1, K.1, p.s.s.o., K.1, turn. 2nd row—P.6 [6, 8], P.2 tog., P.1, turn. 3rd row—K. to last 6 [8, 8] sts., sl.1, K.1, p.s.s.o., K.1, turn. 4th row—P. to last 6 [8, 8] sts., P.2 tog., P.1, turn. 5th row—K. to last 4 [6, 6] sts., sl.1, K.1, p.s.s.p., K.1, turn. 6th row—P. to last 4 [6, 6] sts., P.2 tog., P.1, turn. |
Reference
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