Add to ORKGUsing the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.372, so our new bounds are quite sharp. 57M25; 49Q10, 53A04
We discuss the relationship between polygonal knot energies and smooth knot energies, concentrating ...
The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embe...
AbstractClassical knot theory studies one-dimensional filaments; in this paper we model knots as mor...
Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is...
Abstract. The ropelength of a knot is the quotient of its length by its thick-ness, the radius of th...
The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest e...
AbstractThis paper provides bounds for the ropelength of a link in terms of the crossing numbers of ...
119 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.The Main Theorem shows that e...
A model of the pretzel knot is described. A method for predicting the ropelength of pretzel knots ...
Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered...
A physical interpretation of the rope simulated by the SONO algorithm is presented. Properties of th...
AbstractGiven a “short” piece of rope, one can tie only “simple” knots. We make this precise by mode...
ABSTRACT. We present new computations of approximately length-minimizing polygons with fixed thickne...
We present new computations of approximately length-minimizing polygons with fixed thickness. These ...
Classical knot theory studies one-dimensional filaments; in this paper we model knots as more physic...
We discuss the relationship between polygonal knot energies and smooth knot energies, concentrating ...
The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embe...
AbstractClassical knot theory studies one-dimensional filaments; in this paper we model knots as mor...
Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is...
Abstract. The ropelength of a knot is the quotient of its length by its thick-ness, the radius of th...
The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest e...
AbstractThis paper provides bounds for the ropelength of a link in terms of the crossing numbers of ...
119 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.The Main Theorem shows that e...
A model of the pretzel knot is described. A method for predicting the ropelength of pretzel knots ...
Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered...
A physical interpretation of the rope simulated by the SONO algorithm is presented. Properties of th...
AbstractGiven a “short” piece of rope, one can tie only “simple” knots. We make this precise by mode...
ABSTRACT. We present new computations of approximately length-minimizing polygons with fixed thickne...
We present new computations of approximately length-minimizing polygons with fixed thickness. These ...
Classical knot theory studies one-dimensional filaments; in this paper we model knots as more physic...
We discuss the relationship between polygonal knot energies and smooth knot energies, concentrating ...
The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embe...
AbstractClassical knot theory studies one-dimensional filaments; in this paper we model knots as mor...
