Turk's-head Knots (Braided Band Knots) a Mathematical Modeling
Skip Pennock (2005)
Visual Mathematics
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Skip Pennock (2005)
Visual Mathematics
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Dennis Roseman (1975)
Fundamenta Mathematicae
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Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
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Mulazzani, Michele (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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P. V. Koseleff, D. Pecker (2014)
Banach Center Publications
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We show that every knot can be realized as a billiard trajectory in a convex prism. This proves a conjecture of Jones and Przytycki.
Monica Meissen (1998)
Banach Center Publications
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The minimal number of edges required to form a knot or link of type K is the edge number of K, and is denoted e(K). When knots are drawn with edges, they are appropriately called piecewise-linear or PL knots. This paper presents some edge number results for PL knots. Included are illustrations of and integer coordinates for the vertices of several prime PL knots.
Richard Hartley (1980)
Mathematische Zeitschrift
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Vaughan Jones, Józef Przytycki (1998)
Banach Center Publications
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We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
C.McA. Gordon (1981)
Mathematische Annalen
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Perko, Kenneth A. jr. (1979)
Portugaliae mathematica
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Mohamed Ait Nouh, Akira Yasuhara (2001)
Revista Matemática Complutense
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We give a necessary condition for a torus knot to be untied by a single twisting. By using this result, we give infinitely many torus knots that cannot be untied by a single twisting.