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Mathematical theory of closed curves in three-dimensional space. The number of times and the manner in which a curve crosses itself distinguish different knots. The fewest possible crossings is three, for the overhand (trefoil) knot, which occurs in two mirror versions according to the directions in which the curve crosses itself. Knot theory has been used to understand both atomic and molecular structures (protein folding).
This entry comes from Encyclopædia Britannica Concise. For the full entry on knot theory, visit Britannica.com.