knot: Quick Facts

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Several types of knots

Mathematical knotsKnots are characterized by the number of times and the manner in which the strand crosses itself. A basic loop, which has no crossings and forms only one distinct “knot,” is the simplest knot in knot theory. The number of distinct knots greatly increases with the number of crossings; only those with seven or fewer crossings are shown here.

In knot theory, knots are formed by seamlessly merging the ends of a segment to form a closed loop. Knots are then characterized by the number of times and the manner in which the segment crosses itself. After the basic loop, the simplest knot is the trefoil knot, which is the only knot, other than its mirror image, that can be formed with exactly three crossings.

Examples of common knots.

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