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32:. Each realization of a link or knot has a thickness assigned to it. The thickness τ of a link allows us to introduce a scale with respect to which we can then define the
258:"O. Gonzalez, J.H. Maddocks, "Global Curvature, Thickness and the Ideal Shapes of Knots", Proc. National Academy of Sciences of the USA 96 (1999) 4769–4773"
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169:). From this definition we can deduce that the local thickness is at most equal to the local radius of curvature.
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There exist several possible definitions of thickness that coincide for smooth enough curves.
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Litherland, R. A.; Simon, J.; Durumeric, O.; Rawdon, E. (1999-02-24). "Thickness of knots".
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The thickness is defined using the simpler concept of the local thickness τ(
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141:are points on the link, all distinct, and
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119:{\displaystyle \tau (x)=\inf r(x,y,z),\,}
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218:{\displaystyle \tau (L)=\inf \tau (x).}
172:The thickness of a link is defined as
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237:to the link with radius equal to τ(
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233:This definition ensures that a
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296:10.1016/S0166-8641(97)00210-1
284:Topology and Its Applications
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60:on the link is defined as
48:Global radius of curvature
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28:can have an assigned
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229:Injectivity radius
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30:knot thickness
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264:on 2011-07-06
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266:. Retrieved
262:the original
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315:Knot theory
235:normal tube
36:of a link.
18:knot theory
268:2009-05-08
245:References
40:Definition
34:ropelength
201:τ
183:τ
71:τ
309:Category
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20:, each
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129:where
26:knot
24:and
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