A Knotty Tale: From Vortex Atoms to DNA Tangles
The unexpected discovery more than two decades ago of several new ways to distinguish mathematical knots precipitated a surge of interest in knot theory. Today, intriguing links between knots and physics and illuminating biological applications testify to the new importance of a mathematical pursuit that began in the 19th century with the search for a new atomic theory.
Online Bibliography
Knots
Adams, C.C. 2004. Why Knot? An Introduction to the Mathematical Theory of Knots. Key College Publishing.
______. 2001. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman.
Alexander, J.W. 1928. Topological invariants of knots and links. Transactions of the American Mathematical Society 30:275-306.
Budworth, G. 1985. The Knot Book. New York: Sterling Publishing.
Burton, Jr. , K.S. 1998. Knots: A Step-by-Step Guide to Tying Loops, Hitches, Bends, and Dozens of Other Useful Knots. Philadelphia: Running Press.
Gardner, M. 1997. The topology of knots. In The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications. New York: Copernicus.
Jones, V. 1990. Knot theory and statistical mechanics. Scientific American 262(November):98-103.
Hoste, J., M. Thistlethwaite, and J. Weeks. 1998. The first 1,701,936 knots. Mathematical Intelligencer 20:33-48.
Kauffman, L.H. 1987. On Knots. Princeton University Press.
Lindley, D. 2004. Degrees Kelvin: A Tale of Genius, Invention, and Tragedy. Washington, D.C.: Joseph Henry Press.
Neuwirth, L. 1979. The theory of knots. Scientific American 240 (June):110-124.
Peterson, I. 2006. Knots in proteins. Science News Online (Oct. 14).
______. 2006. Knot physics of old. Science News Online (Feb. 24).
______. 2005. Tying down a random walk. MAA Online (Sept. 26).
______. 2005. Knotted strings and Inca accounts. MAA Online (Aug. 22).
______. 2003. The tangled task of distinguishing knots. MAA Online (Feb. 24).
______. 2003. Knotty calculations. Science News 163(Feb. 22):124-125.
______. 1992. Knotty views. Science News 141(March 21):186-187.
______. 1988. Unknotting a tangled tale. Science News 133(May 21):328-329.
Przytycki, J.H. Preprint. Knot theory from Vandermonde to Jones.
Silver, D.S. 2006. Knot theory's odd origins. American Scientist 94(March-April):158-165.
Knot News
Brown, S. 2008. Scientists discover DNA knot keeps viral genes tightly corked inside shell. UC San Diego News Center (June 17).
Rehmeyer, J. 2008. Detangling DNA. Science News (May 23).
Other Resources
A remarkably complete guide to "Knots on the Web" can be found at http://www.earlham.edu/~peters/knotlink.htm.
"Mathematics and Knots" at http://www.popmath.org.uk/exhib/knotexhib.html presents a grand visual tour of knots and their curious properties.
Topology and Scottish Mathematical Physics
Untangle the mathematics of knots at http://www.c3.lanl.gov/mega-math/workbk/knot/knot.html.
