Projections of knots
Dennis Roseman (1975)
Fundamenta Mathematicae
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Dennis Roseman (1975)
Fundamenta Mathematicae
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Skip Pennock (2004)
Visual Mathematics
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Skip Pennock (2005)
Visual Mathematics
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Mulazzani, Michele (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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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.
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.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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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.
Perko, Kenneth A. jr. (1979)
Portugaliae mathematica
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Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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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.
Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
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