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Ruler and Compass Constructions of the Equilateral Triangle and Pentagon in the Lemniscate Curve

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References

  1. A. Bogomolny. Cut the Knot: Geometric Construction of Roots of Quadratic Equation. https://www.cut-the-knot.org/Curriculum/Algebra/QuadraticRoots.shtml.

  2. D. A. Cox and T. Hyde. The Galois theory of the lemniscate. Journal of Number Theory  135 (2014), 43–59.

  3. M. A. Gómez-Molleda and J.-C. Lario. Practical geometric constructions with ruler and compass in the lemniscate curve. Preprint, 2019.

  4. M. Rosen. Abel’s theorem on the lemniscate. American Mathematical Monthly  88:6 (1981), 387–395.

  5. N. Schappacher. Some milestones of lemniscatomy. In Algebraic Geometry (Ankara, 1995), pp. 257–290, Lecture Notes in Pure and Appl. Math. 193. Dekker, 1997.

  6. J. Stillwell. Mathematics and Its History (third edition), Chapter 12: “Elliptic Functions,” Undergraduate Texts in Mathematics. Springer, 2010.

  7. A. Sutton. Ruler and Compass. Practical Geometric Constructions. Bloomsbury, 2009.

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Authors and Affiliations

  1. Universidad de Málaga, Málaga, Spain

    M. A. Gómez-Molleda

  2. Universitat Politècnica de Catalunya, Barcelona, Spain

    Joan-C. Lario

Authors
  1. M. A. Gómez-Molleda
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  2. Joan-C. Lario
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Correspondence to Joan-C. Lario.

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Gómez-Molleda, M.A., Lario, JC. Ruler and Compass Constructions of the Equilateral Triangle and Pentagon in the Lemniscate Curve. Math Intelligencer 41, 17–21 (2019). https://doi.org/10.1007/s00283-019-09892-w

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  • DOI: https://doi.org/10.1007/s00283-019-09892-w

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