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- W2116729181 abstract "A Chebyshev knot C ( a , b , c , φ ) is a knot which has a parametrization of the form x ( t ) = T a ( t ) ; y ( t ) = T b ( t ) ; z ( t ) = T c ( t + φ ) , where a , b , c are integers, T n ( t ) is the Chebyshev polynomial of degree n and φ ∈ R . We show that any rational knot is a Chebyshev knot with a = 3 and also with a = 4 . For every a , b , c integers ( a = 3 , 4 and a , b coprime), we describe an algorithm that gives all Chebyshev knots C ( a , b , c , φ ) . We deduce the list of minimal Chebyshev representations of rational knots with 10 or fewer crossings." @default.
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- W2116729181 date "2010-12-01" @default.
- W2116729181 modified "2023-10-01" @default.
- W2116729181 title "The first rational Chebyshev knots" @default.
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- W2116729181 doi "https://doi.org/10.1016/j.jsc.2010.06.014" @default.
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