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Three linked but pairwise separated rings
one that can be formed from three convex curves. In knot theory, the ropelength of a knot or link is the shortest length of flexible rope (of radius one)
Borromean_rings
Knot invariant
physical knot theory, each realization of a link or knot has an associated ropelength. Intuitively this is the minimal length of an ideally flexible rope that
Ropelength
Simplest nontrivial knot link
other. This model minimizes the ropelength of the link and until 2002 the Hopf link was the only link whose ropelength was known. The convex hull of these
Hopf_link
transformation taking it to a Voronoi diagram? Ropelength problems: Is there a general expression for the minimum ropelength of an arbitrary closed knot? What constant
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Line through four points of a curve
connection with knot invariants including the minimum total curvature and the ropelength of a knot. The number of quadrisecants of a non-singular algebraic curve
Quadrisecant
us to introduce a scale with respect to which we can then define the ropelength of a link. There exist several possible definitions of thickness that
Knot_thickness
Function of a knot that takes the same value for equivalent knots
\oint _{K}\kappa \,ds>4\pi .\,} An example of a "physical" invariant is ropelength, which is the length of unit-diameter rope needed to realize a particular
Knot_invariant
Study of mathematical models of knotting phenomena
specific embeddings ("conformations") of the circle. Such properties include ropelength and various knot energies (O’Hara 2003). Most of the work discussed in
Physical_knot_theory
Particular knot energy
Möbius energy of 74.88, close to the minimum of 74.41 . The knot on the right has close to the minimum ropelength, but a higher Möbius energy of 78.06.
Möbius_energy
Ernst, C.; Por, A. (2012), "Average crossing number, total curvature and ropelength of thick knots", Journal of Knot Theory and Its Ramifications, 21 (3):
Average_crossing_number
invariant Linking number Milnor invariants Racks and quandles and Biquandle Ropelength Seifert surface Self-linking number Signature of a knot Skein relation
List_of_knot_theory_topics
Ice climbing on ice and rock surfaces
it off a year or two. The reason is, of course, that [climbing] a full ropelength of horizontal roof on tiny hooks is relatively easy". While the evolution
Mixed_climbing
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