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knot theory

   Also found in: Wikipedia 0.02 sec.

knot theory

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).



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Molecular biologists are faced with an unprecedented quantity of data as a result of new technologies requiring the use of advanced computational techniques from unfamiliar areas of mathematics such as computer science, knot theory, and graph theory, whereas proteomics requires combinatorial geometry, thermodynamics, and other areas of physics and chemistry.
In the past decade, however, mathematicians have turned knot theory into a bridge between two seemingly unconnected subjects: computer science and quantum mechanics, the branch of physics that deals with the ultrasmall scale of atoms and subatomic particles.
won the third-place $50,000 scholarship for his study of knot theory, an area of mathematics which examines closed curves in three-dimensional space and has applications in genetic research.
 
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