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What Should a Surface in 4-Space Look Like?

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Visualization and Mathematics

Summary

We wish to investigate spaces of dimension greater than three and in particular surfaces in 4-dimensional space. Such surfaces can be knotted. Our explorations include mathematical and visualization tools.

Mathematically we focus on a particular example of visualization of the result of an energy flow of a knotted surface. In terms of visualization, we use sound, texture, and a slicing technique of “splayed slabs”, in addition to more traditional tools.

Basic issues of the mathematical visualization process are discussed.

Partially supported by NSF grant DMS-9505087

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Authors and Affiliations

  1. Department of Mathematics, University of Iowa, Iowa City, Iowa, USA

    Dennis Roseman

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  1. Dennis Roseman
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Editors and Affiliations

  1. Wissenschaftliche Visualisierung, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustraße 7, D-14195, Berlin, Germany

    Hans-Christian Hege

  2. Fachbereich 3, Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany

    Konrad Polthier

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© 1997 Springer-Verlag Berlin Heidelberg

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Roseman, D. (1997). What Should a Surface in 4-Space Look Like?. In: Hege, HC., Polthier, K. (eds) Visualization and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59195-2_5

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  • DOI: https://doi.org/10.1007/978-3-642-59195-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63891-6

  • Online ISBN: 978-3-642-59195-2

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