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Interactive Knot Theory with KnotPlot

  • Conference paper
Multimedia Tools for Communicating Mathematics

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

We describe the computer program KnotPlot, a topological drawing tool for knots and links. Novel aspects of KnotPlot include interactive construction and manipulation of a large variety of knots and their embeddings into three-space, automated and semi-automated knot relaxation and simplification algorithms, and techniques for calculating and converting among a number of mathematical representations for knots in addition to direct visualization of the embeddings. Some applications of the system to knot theoretical problems are discussed, including the determination of the stick number of a knot and simplification of complex hyperbolic knots.

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Author information

Authors and Affiliations

  1. Media and Graphics Interdisciplinary Centre (MAGIC), University of British Columbia, Vancouver, BC, Canada

    Robert G. Scharein & Kellogg S. Booth

  2. Pacific Institute for Mathematical Sciences (PIMS), Vancouver, BC, Canada

    Robert G. Scharein

Authors
  1. Robert G. Scharein
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  2. Kellogg S. Booth
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Editor information

Editors and Affiliations

  1. Centre for Experimental and Constructive Mathematics, Simon Fraser University, Burnaby, BC, Canada, V5A 1S6

    Jonathan Borwein

  2. CMAF, University of Lisbon, Av. Prof. Gama Pinto 2, 1649-003, Lisbon, Portugal

    Maria H. Morales  & José F. Rodrigues  & 

  3. FB 3 Mathematics, Technical University Berlin, MA 8-3, Straße des 17. Juni 136, 10623, Berlin, Germany

    Konrad Polthier

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© 2002 Springer-Verlag Berlin Heidelberg

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Cite this paper

Scharein, R.G., Booth, K.S. (2002). Interactive Knot Theory with KnotPlot. In: Borwein, J., Morales, M.H., Rodrigues, J.F., Polthier, K. (eds) Multimedia Tools for Communicating Mathematics. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56240-2_17

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  • DOI: https://doi.org/10.1007/978-3-642-56240-2_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62701-9

  • Online ISBN: 978-3-642-56240-2

  • eBook Packages: Springer Book Archive

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