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Surprise Meeting: Euclidean Algorithm and Geometric Constructions

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Abstract

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.

Mathematics is rife with the usage of some of its concepts in the study of other ones when these concepts belong to its very different branches. The article presents an example of such a surprising meeting—the use of the Euclidean algorithm in geometric constructions with the help of just a straightedge. The article can be used to enrich mathematical activities in high school and by teachers and students of classical geometry in colleges and universities.

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Suggested Reading

  1. A S Smogorzhevskii, The Ruler in Geometrical Constructions, New York: Blaisdell, 1961.

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  2. V Oxman, M Stupel and A Sigler, Geometrical shapes allowing the construction of the midpoint of a segment using a straightedge only, Journal for Geometry and Graphics, Vol.20, No.1, pp.75–83, 2016.

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  3. R A Johnson, Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle, Houghton Mifflin, Boston MA 1929.

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  4. A S Posamentier, C T Salkind, Challenging Problems in Geometry, Dover Publishing Co., Second revised edition, 1996.

  5. R Courant, H Robbins, What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed., Oxford, England: Oxford University Press, 1996.

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Author information

Authors and Affiliations

  1. Shaanan College, Haifa, Israel

    Victor Oxman

  2. Western Galilee College, Acre, Israel

    Victor Oxman

  3. Shaanan College, Haifa, Israel

    Avi Sigler

Authors
  1. Victor Oxman
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  2. Avi Sigler
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Corresponding authors

Correspondence to Victor Oxman or Avi Sigler.

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No potential conflict of interest was reported by the authors.

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Cite this article

Oxman, V., Sigler, A. Surprise Meeting: Euclidean Algorithm and Geometric Constructions. Reson 27, 435–442 (2022). https://doi.org/10.1007/s12045-022-1331-4

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  • DOI: https://doi.org/10.1007/s12045-022-1331-4

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