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CHEBYSHEV KNOTS

Université Pierre et Marie Curie, INRIA-Paris-Rocquencourt Salsa, and Laboratoire d'Informatique de Paris 6, CNRS (UMR 7606) 4, Place Jussieu, F-75252 Paris Cedex 05, France

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D. PECKER

Université Pierre et Marie Curie, 4, Place Jussieu, F-75252 Paris Cedex 05, France

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https://doi.org/10.1142/S0218216511009364Cited by:15 (Source: Crossref)

Abstract

A Chebyshev knot is a knot which admits 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 integers, T_n(t) is the Chebyshev polynomial of degree n, and φ ∈ R. Chebyshev knots are non-compact analogues of the classical Lissajous knots. We show that there are infinitely many Chebyshev knots with φ = 0. We also show that every knot is a Chebyshev knot.

Keywords:

AMSC: 14H50, 57M25, 14P99

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Vol. 20, No. 04

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Accepted 11 December 2009

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CHEBYSHEV KNOTS

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