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Explorations with Sketchpad in Topogeometry

  • Computer Math Snapshots. Editor—Uri Wilensky*
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Notes

  1. This tool simply adds an additional constraint on the locus created for the Torus Circle, which is to say, the locus only exists when its’ closest path to the centre is equal to the given radius.

  2. The Sketchpad file containing the three microworlds described in this paper can be found on-line at http://www.sfu.ca/~nathsinc/gsp/topology.zip

References

  • Jackiw , N. (1991, 2001). The Geometer’s Sketchpad ®. Emeryville, CA: Key Curriculum Press.

  • Jackiw, N. (1997). Drawing worlds: Scripted exploration environments in the Geometer’s Sketchpad ®. In J. R. King & D. Schattschneider (Eds.), Geometry turned on!: Dynamic software in learning, teaching, and research (pp. 179–184). Washington, DC: The Mathematical Association of America.

  • Meyerhoff, R. (1992). Geometric invariants for 3-manifolds. The Mathematical Intelligencer, 14(1), 37–53.

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  • Weeks, J. (2001). Exploring the shape of space. Emeryville, CA: Key Curriculum Press.

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Acknowledgments

We would like to thank Ronald Fintushel and Robert R. Bruner for answering our many topological questions and Nicholas Jackiw for answering our many Sketchpad questions. We would also like to thank our anonymous reviewer for suggesting the term ‘topogeometry.’

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Authors and Affiliations

  1. Michigan State University, 8462 Pine Creek Drive, Shelby Township, MI, 48316, USA

    Amanda Hawkins

  2. Simon Fraser University, Burnaby, BC, Canada

    Nathalie Sinclair

Authors
  1. Amanda Hawkins
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  2. Nathalie Sinclair
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Correspondence to Amanda Hawkins.

Additional information

*This column will publish short (from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain-teasers involving the use of computers or computational theory. Snapshots are subject to peer review.

This innovative snapshot uses Geometric Sketchpad to create a series of microworlds for representing and exploring standard topological surfaces such as the Torus, Klein bottle and Mobius strip. Using differing strategies of “wraparound”, these surfaces can be explored in their 2D flat representations. Using a dot on the leading edge of a sketchpad ray as the driver for the exploration, the authors call this domain “topogeometry”. Several interesting topogeometric questions are explored and visualized.

From the Column Editor Uri Wilensky, Northwestern University. e-mail: uri@northwestern.edu

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Hawkins, A., Sinclair, N. Explorations with Sketchpad in Topogeometry. Int J Comput Math Learning 13, 71–82 (2008). https://doi.org/10.1007/s10758-008-9126-6

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  • DOI: https://doi.org/10.1007/s10758-008-9126-6

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