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Two knots are equivalent if one can be transformed into
the other without breaking the curve at any time. For example,
any knot that can be transformed into a perfect circle is considered to be
equivalent to that circle from the point of view of knot theory. The perfect circle,
and anything equivalent to it, is called an unknot or trivial
knot. A nontrivial knot refers to any knot that is not equivalent
to a circle.
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