In mathematics, a stuck unknot is a closed polygonal chain in three-dimensional space (a skew polygon) that is topologically equal to the unknot but cannot be deformed to a simple polygon when interpreted as a mechanical linkage, by rigid length-preserving and non-self-intersecting motions of its segments.[1][2] Similarly a stuck open chain is an open polygonal chain such that the segments may not be aligned by moving rigidly its segments. Topologically such a chain can be unknotted, but the limitation of using only rigid motions of the segments can create nontrivial knots in such a chain.
^G. Aloupis, G. Ewald, and G. T. Toussaint, "More classes of stuck unknotted hexagons," Contributions to Algebra and Geometry, Vol. 45, No. 2, 2004, pp. 429–434.
^G. T. Toussaint, "A new class of stuck unknots in Pol-6," Contributions to Algebra and Geometry, Vol. 42, No. 2, 2001, pp. 301–306.
stuck, unknot, mathematics, stuck, unknot, closed, polygonal, chain, three, dimensional, space, skew, polygon, that, topologically, equal, unknot, cannot, deformed, simple, polygon, when, interpreted, mechanical, linkage, rigid, length, preserving, self, inter. In mathematics a stuck unknot is a closed polygonal chain in three dimensional space a skew polygon that is topologically equal to the unknot but cannot be deformed to a simple polygon when interpreted as a mechanical linkage by rigid length preserving and non self intersecting motions of its segments 1 2 Similarly a stuck open chain is an open polygonal chain such that the segments may not be aligned by moving rigidly its segments Topologically such a chain can be unknotted but the limitation of using only rigid motions of the segments can create nontrivial knots in such a chain Consideration of such stuck configurations arises in the study of molecular chains in biochemistry References edit G Aloupis G Ewald and G T Toussaint More classes of stuck unknotted hexagons Contributions to Algebra and Geometry Vol 45 No 2 2004 pp 429 434 G T Toussaint A new class of stuck unknots in Pol 6 Contributions to Algebra and Geometry Vol 42 No 2 2001 pp 301 306 nbsp This knot theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Stuck unknot amp oldid 1165855685, wikipedia, wiki, book, books, library,
