Knots and Knot Types
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Almost everyone is familiar with at least the simplest of the common knots, e.g., the overhand knot, Figure 1, and the figure-eight knot, Figure 2. A little experimenting with a piece of rope will convince anyone that these two knots are different: one cannot be transformed into the other without passing a loop over one of the ends, i.e., without “tying” or “untying.” Nevertheless, failure to change the figure-eight into the overhand by hours of patient twisting is no proof that it can’t be done. The problem that we shall consider is the problem of showing mathematically that these knots (and many others) are distinct from one another.
KeywordsMultiple Point Double Point Orientation Preserve Infinite Order Mathematical Definition
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