@String{http = "http://CRAN.R-project.org/doc/Rnews/"}
@String{Rnews2006-2 = "http://CRAN.R-project.org/doc/Rnews/Rnews_2006-2.pdf"}
@String{Rnews2008-1 = "http://CRAN.R-project.org/doc/Rnews/Rnews_2008-1.pdf"}

@article{alexander1926,
	title = {On {Types} of {Knotted} {Curves}},
	volume = {28},
	issn = {0003-486X},
	doi = {10.2307/1968399},
	number = {1/4},
	urldate = {2016-06-17},
	journal = {Annals of Mathematics},
	author = {Alexander, J. W. and Briggs, G. B.},
	year = {1926},
	pages = {562--586}
}
                  
@misc{wikipedia_knot_theory,
    author = "{Wikipedia contributors}",
    title = "Knot theory --- {Wikipedia}{,} The Free Encyclopedia",
    year = "2021",
    url = "https://en.wikipedia.org/w/index.php?title=Knot_theory&oldid=1043464461",
    note = "[Online; accessed 16-September-2021]"
  }

@Manual{olsen2014,
   title = {bezier: Bezier Curve and Spline Toolkit},
   author = {Aaron Olsen},
   year = {2014},
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}

@misc{Inkscape,
  author = {{Inkscape Project}},
  title = {Inkscape software},
  note = {{\tt https://inkscape.org}},
  version = {0.92.5}, 
  date={2020-04-16}
}
                  
@Book{manturov2004,
  author =	 {V. Manturov},
  title = 	 {Knot Theory},
  publisher = 	 {Chapman and Hall},
  year = 	 {2004}
  }

@Manual{hankin2020,
    title = {knotR: Knot Diagrams using Bezier Curves},
    author = {Robin K. S. Hankin},
    note = {R package version 1.0-4, {\tt https://CRAN.R-project.org/package=knotR}},
    year = {2020}
    }

@Manual{rcore2021,
     title = {R: A Language and Environment for Statistical Computing},
     author = {{R Core Team}},
     organization = {R Foundation for Statistical Computing},
     address = {Vienna, Austria},
     year = {2021},
     url = {https://www.R-project.org/}
   }

@article{comoglio2011,
author = {F. Comoglio  and M. Rinaldi},
year = {2011},
title = {A Topological Framework for the Computation of the HOMFLY Polynomial and Its Application to Proteins},
journal = {PLoS ONE},
volume = {6},
number = {4}
}

@article{comoglio2012,
author = {F. Comoglio and M. Rinaldi},
year = {2012},
title = {Rknots: topological analysis of knotted biopolymers with R},
journal = {Bioinformatics},
volume = {28},
number = {10},
pages = {1400--1401}
}

@Article{khorami2020,
  author = 	 {M. Khorami},
  title = 	 {Space harmony: a knot theory perspective on the work of {R}udolph {L}aban},
  journal = 	 {Journal of Mathematics and the Arts},
  year = 	 {2020},
  volume =	 {14},
  number =	 {3},
  pages =	 {239--257}
  }

@Article{bosch2010,
  author = 	 {R. Bosch},
  title = 	 {Simple-closed-curve sculptures of knots and links},
  journal = 	 {Journal of Mathematics and the Arts},
  year = 	 {2010},
  volume =	 {4},
  number =	 {2},
  pages =	 {57--71}
  }

@Article{cromwell2008,
  author = 	 {P. R. Cromwell},
  title = 	 {The distribution of knot types in {C}eltic interlaced ornament},
  journal = 	 {Journal of Mathematics and the Arts},
  year = 	 {2008},
  volume =	 {2},
  number =	 {2},
  pages =	 {61--68}
  }

@Article{widmark2020,
  author = 	 {A. Widmark},
  title = 	 {Stixhexaknot: a symmetric cylinder arrangement of knotted glass},
  journal = 	 {Journal of Mathematics and the Arts},
  year = 	 {2020},
  volume =	 {14},
  number =	 {1-2},
  pages =	 {167--169}
}

@Article{hart2008,
  author = 	 {G. W. Hart and N. Jonoska},
  title = 	 {Knotting mathematics and Art},
  journal = 	 {Journal of Mathematics and the Arts},
  year = 	 {2008},
  volume =	 {2},
  number =	 {1},
  pages =	 {47-51},
  note = {Conference in low-dimensional topology and mathematical art, University of South Florida, Tampa, FL, 1-4 November 2007}
}

@Book{rolfsen1976,
  author =	 {D. Rolfsen},
  title = 	 {Knots and links},
  publisher = 	 {Publish or Perish Press},
  year = 	 {1976}
  }

@Book{adams2004,
  author =	 {C. C. Adams},
  title = 	 {The knot book: an elementary introduction to the mathematical theory of knots},
  publisher = 	 {American Mathematical Society},
  year = 	 {2004}
  }

@Book{bain1973,
  author =	 {G. Bain},
  title = 	 {Celtic art: the methods of instruction},
  publisher = 	 {MacLellan \& Co. (reprinted by Dover)},
  year = 	 {1973}
  }

@Article{tait1884,
  author = 	 {P. G. Tait},
  title = 	 {The first seven orders of knottiness},
  journal = 	 {Transactions of the Royal Society of Edinburg},
  year = 	 {1884},
  volume =	 {32},
  pages =	 {327--342}
  }

@Article{przytycki1998,
  author = 	 {J. H. Przytycki},
  title = 	 {Classical roots of knot theory},
  journal = 	 {Chaos, Solitons \& Fractals},
  year = 	 {1998},
  volume =	 {9},
  number =	 {4/5},
  pages =	 {531--545}
  }

@Misc{knot_atlas,
  title =	 {The Knot atlas},
  howpublished = {online},
  note = {\verb+http://katlas.org/wiki/Main_Page+}
}

@Article{hoste1998,
  author = 	 {J. Hoste and M. Thistlethwaite and J. Weeks},
  title = 	 {The first 1701936 knots},
  journal = 	 {The Mathematical Intelligencer},
  year = 	 {1998},
  volume =	 {20},
  number =	 {4},
  pages =	 {33--48}
  }

@Manual{comoglio2016,
    title = {Rknots: Topological Analysis of Knotted Proteins,
                  Biopolymers and 3{D} Structures},
    author = {Federico Comoglio and Maurizio Rinaldi},
    year = {2016},
    note = {R package version 1.3.2},
    url = {https://CRAN.R-project.org/package=Rknots},
  }

@InProceedings{antonsen2021,
  author = 	 {R. Antonsen and L. Taalman},
  title = 	 {Categorizing {C}eltic knot designs},
  booktitle =    {Bridges 2021 Conference Proceedings},                  
  year =	 {2021},
  pages =	 {87--94},
  month =	 {August},
  address =	 {(Virtual)},
  organization = {The Bridges Organization}
  }

@Misc{taalman2019,
  author =	 {L. Taalman},
  title =	 {Mathematical Art Galleries},
  howpublished = {Online},
  year =	 {2019},
  note = 	 {The Bridges Organization; URL {\tt http://gallery.bridgesmathart.org/exhibitions/2019-icerm-illustrating-mathematics/laura-taalman}},
}

@Article{irvine2020,
  author = 	 {V. Irvine and T. Biedl and C. S. Kaplan},
  title = 	 {Quasiperiodic bobbin lace patterns},
  journal = 	 {Journal of Mathematics and the Arts},
  year = 	 {2020},
  volume =	 {14},
  number =	 {3},
  pages =	 {177--198}
  }

@Misc{scharein1998,
  author = 	 {R. G. Scharein},
  title = 	 {Interactive topological drawing},
  school = 	 {The University of British Columbia},
  year = 	 {1998},
  howpublished = {PhD thesis online at {\tt https://open.library.ubc.ca/soa/cIRcle/collections/ubctheses/831/items/1.0051670}}
  }

@Misc{scharein1997,
  author =	 {R. G. Scharein},
  title = 	 {KnotPlot - A Program for Viewing Mathematical Knots},
  howpublished = {online; {\tt http://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.html}},
  year =	 {1997}
  }

@Manual{brunner2021,
    title = {generativeart: Create Generative Art with R},
    author = {Katharina Brunner},
    year = {2021},
    note = {R package version 1.0, online {\tt https://katharinabrunner.de/2018/11/r-package-to-create-generative-art/}}
  }

 @Article{nelder1965,
  author = 	 {J. A. Nelder and R. Mead},
  title = 	 {A simplex algorithm for function minimization},
  journal = 	 {Computer Journal},
  year = 	 {1965},
  volume =	 {7},
  pages =	 {308--313}
  }
                  
 @Book{dennis1983,
  author =	 {J. E. Dennis and R. B. Schnabel},
  title = 	 {Numerical methods for unconstrained optimization and nonlinear equations},
  publisher = 	 {Prentice-Hall},
  year = 	 {1983},
  address =	 {Englewood Cliffs, NJ}
  }