TITLE: The Figure 8 Knot
AUTHORS: P. Boyland & S. Dickson
SOFTWARE: Mathematica®
SOURCE: Mathematica® 2.2 Examples
COMMENTS:
A mathematical knot is a closed curve embedded in three-dimensional space. A knotted piece of string with the ends joined is a good physical model for a knot. If you were given two physical knots and you could manipulate one (without cutting the strings) and make it look exactly like the other, you would call them the same knot. The mathematical analog of this "sameness" is called knot equivalence.
The classification of knots up to knot equivalence is the central problem in the mathematical theory of knots. There are two parts to the classification. First, given two apparently different knots, you must have a procedure to decide whether they are in fact equivalent. Second, there has to be a system of names or labels for the various equivalence classes of knots. Certain simple knots are labeled by their traditional names like figure eight (shown in the figure), overhand, or cloverleaf. (Knot Theory, excerpts from the notebook section titled "Discussion")
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Get the code
(Mathematica® 4 notebook) to create similar graphics. This program was
an example given with Mathematica®
2.2, Copyright 1991-93
Wolfram Research, Inc. |
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