A mathematical knot is a knot that cannot be undone because the ends are joined together. In math lingo, a mathematical knot is a "embedding of a circle in 3-D Euclidean space." Two knots are equivalent if they can be transformed from one form to another via a deformation of R^3 upon itself. This basically means that if the knot could be transformed to the second know without cutting the string of passing through the string itself, then the knots are equivalent.
Here is an picture of one of the simplest types of mathematical knots, called a trefoil knot.
This a more complex mathematical knot.
Math joke of the day:
Wow that is phenomenal, great post. The joke always makes me chuckle a little.
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