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Problem of the Week 851

Lattice Tie a Knot

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A knot is a closed curve (non-self-intersecting) that cannot be deformed into a simple loop.

Consider curves obtained by using straight segments of unit length from a lattice point to a neighboring lattice point in 3-space. It is easy to make a loop having length 6, and of course a simple little square is a loop of length 4.

What is the shortest knot you can find using curves of this sort?

© Copyright 1997 Stan Wagon. Reproduced with permission.

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The Math Forum

2 October 1998