RIBBONLENGTH OF TORUS KNOTS
2008 ◽
Vol 17
(01)
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pp. 13-23
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Using Kauffman's model of flat knotted ribbons, we demonstrate how all regular polygons of at least seven sides can be realized by ribbon constructions of torus knots. We calculate length to width ratios for these constructions thereby bounding the Ribbonlength of the knots. In particular, we give evidence that the closed (respectively, truncation) Ribbonlength of a (q + 1,q) torus knot is (2q + 1) cot (π/(2q + 1)) (respectively, 2q cot (π/(2q + 1))). Using these calculations, we provide the bounds c1 ≤ 2/π and c2 ≥ 5/3 cot π/5 for the constants c1 and c2 that relate Ribbonlength R(K) and crossing number C(K) in a conjecture of Kusner: c1 C(K) ≤ R(K) ≤ c2 C(K).
2007 ◽
Vol 16
(08)
◽
pp. 1043-1051
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2011 ◽
Vol 20
(12)
◽
pp. 1723-1739
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Keyword(s):
2019 ◽
Vol 28
(03)
◽
pp. 1950023
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2008 ◽
Vol 17
(10)
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pp. 1175-1187
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FUNDAMENTAL BIQUANDLES OF RIBBON 2-KNOTS AND RIBBON TORUS-KNOTS WITH ISOMORPHIC FUNDAMENTAL QUANDLES
2014 ◽
Vol 23
(01)
◽
pp. 1450001
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1995 ◽
Vol 117
(1)
◽
pp. 129-135
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2013 ◽
Vol 22
(08)
◽
pp. 1350041
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