Daily Archives: April 6, 2008

Ashley knots; ABOK #2217 covering knot

For those of you who aren’t familiar with blue collar knots, “ABOK” means “The Ashley Book of Knots,” an ecyclopedic book on knots written in 1944 that has since become the reference for knot identification. I think it was my maternal grandfather that gave me my, somewhat rare, now the worse from love and use, 1st edition copy back in the 1960s; but what with the natural self-naturedness of a boy I cannot recall for sure. #2217 refers to a particularly handsome knot in the chapter “The Monkey’s Fist and Other Knot Coverings.” To justify “handsome” requires a sample photo from cbrew6 on Knot Heads World Wide:
Ashley book of Knots #2217 tied by cbrew6 as shown on Knot Heads World Wide

This knot is “tied on the table,” which means that one uses a diagram to draw it. From a topological point of view, a table diagram in this case is a mapping of the surface of the sphere to the plane. A line drawing shows the path that the cord takes. The path is a loop, that is, it ends at the same point at which it starts. The path is restricted to never cross itself twice at a single point. At each crossing, some sort of notation indicates which line is to be on top, but for planar knots like the above, it is arranged so that the cord will weave over, under, over, under … And it is a trivial fact of practical folks topology that one can always assign such a pattern.
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