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Close cousins - Knots vs. Links

Image borrome
Is the figure to the above a knot?

Sometimes we run into figures that cannot be classified as knots. This figure at the right looks kind of like a knot, but we no longer have a simple closed curve - we have a group of simple closed curves (three separate loops). The new figure is called a link.

A link is a collection of knots; the individual knots which make up a link are called the components of the link. This specific link shown above is known as the Borromean Rings.

An interesting fact about the Borromean Rings: If you remove one of the component loops, the other two loops will no longer be connected! An interesting question: Can the Borromean Rings be formed using 3 flat closed loops?

Just as mathematicians try to untangle knots to form the unknot, we try to separate links to form the "unlink". A link is referred to as splittable if the component loops can be separated without cutting.


next up previous
Next: About this document ... Up: text_knot Previous: Conway's Notation
Supriya Garg 2004-05-02