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Knots are familiar shapes yet can be dauntingly mysterious (especially when trying to untangle a messy one).  Knowledge of some knot formations is a necessity for sailors, yet there is much we don’t know about knots – so mathematicians study “knot theory.”  

Mathematical knots are closed.  They do not have two loose ends, like shoelaces that can be untied.  To make the simplest mathematical knot, take a length of string or flexible wire and bend it so the two ends cross each other.  Now take the end that is “on top” and twist it to go under, then over the other end.  Finally, glue the two ends together.  This is called a trefoil knot.  In its most symmetric presentation, it looks like three identical rings woven together.  It is impossible to undo this or any mathematical knot without cutting it.

When Bakker gives instructions to his computer program to connect copies of a polyline generator in order to form closed circuits in space, some of the circuits among the thousands produced may be mathematical knots.  The program contains a filter that can identify which of the circuits are knots, and from these the artist can select what becomes the basis for a knotted sculpture.

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