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Quadrilaterals as Geometric Loci

Year 2022, Volume: 15 Issue: 2, 321 - 333, 31.10.2022

Lorenz Halbeısen Norbert Hungerbühler Juan Läuchli

https://doi.org/10.36890/iejg.1062741

Abstract

We give necessary and sufficient conditions, both algebraic and geometric, for a quadrilateral to be the level set of the sum of the distances to m ≥ 2 different lines.

Keywords

Quadrilaterals geometric locus harmonic points

References

  • [1] Elias Abboud. Viviani’s theorem and its extension. College Math. J., 41(3):203– 211, 2010.
  • [2] Henk J. M. Bos. Redefining geometrical exactness. Descartes’ transformation of the early modern concept of construction. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, 2001.
  • [3] Christoph Gudermann. Grundriss der analytischen Sphärik. DuMont-Schauberg, Köln, 1830.
  • [4] Lorenz Halbeisen, Norbert Hungerbühler, and Juan Läuchli. Mit harmonischen Verhältnissen zu Kegelschnitten. Perlen der klassischen Geometrie. Springer Spektrum, Berlin, 2021.
  • [5] Norbert Hungerbühler and Gerhard Wanner. Ceva-triangular points of a triangle. Elem. Math., 2021, published online first.
  • [6] Wei Lai and Weng Kin Ho. Graphing a quadrilateral using a single cartesian equation. In Electronic Proceedings of the 22nd Asian Technology Conference in Mathematics, Chung Yuan Christian University, Chungli, Taiwan, December 15–19 2017. Mathematics and Technology, LLC.

Year 2022, Volume: 15 Issue: 2, 321 - 333, 31.10.2022

Lorenz Halbeısen Norbert Hungerbühler Juan Läuchli

https://doi.org/10.36890/iejg.1062741

Abstract

References

  • [1] Elias Abboud. Viviani’s theorem and its extension. College Math. J., 41(3):203– 211, 2010.
  • [2] Henk J. M. Bos. Redefining geometrical exactness. Descartes’ transformation of the early modern concept of construction. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, 2001.
  • [3] Christoph Gudermann. Grundriss der analytischen Sphärik. DuMont-Schauberg, Köln, 1830.
  • [4] Lorenz Halbeisen, Norbert Hungerbühler, and Juan Läuchli. Mit harmonischen Verhältnissen zu Kegelschnitten. Perlen der klassischen Geometrie. Springer Spektrum, Berlin, 2021.
  • [5] Norbert Hungerbühler and Gerhard Wanner. Ceva-triangular points of a triangle. Elem. Math., 2021, published online first.
  • [6] Wei Lai and Weng Kin Ho. Graphing a quadrilateral using a single cartesian equation. In Electronic Proceedings of the 22nd Asian Technology Conference in Mathematics, Chung Yuan Christian University, Chungli, Taiwan, December 15–19 2017. Mathematics and Technology, LLC.
There are 6 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Lorenz Halbeısen 0000-0001-6078-7237

Norbert Hungerbühler 0000-0001-6191-0022

Juan Läuchli This is me 0000-0001-6200-7708

Early Pub Date July 23, 2022
Publication Date October 31, 2022
Acceptance Date October 18, 2022
Published in Issue Year 2022 Volume: 15 Issue: 2

Cite

APA Halbeısen, L., Hungerbühler, N., & Läuchli, J. (2022). Quadrilaterals as Geometric Loci. International Electronic Journal of Geometry, 15(2), 321-333. https://doi.org/10.36890/iejg.1062741
AMA Halbeısen L, Hungerbühler N, Läuchli J. Quadrilaterals as Geometric Loci. Int. Electron. J. Geom. October 2022;15(2):321-333. doi:10.36890/iejg.1062741
Chicago Halbeısen, Lorenz, Norbert Hungerbühler, and Juan Läuchli. “Quadrilaterals As Geometric Loci”. International Electronic Journal of Geometry 15, no. 2 (October 2022): 321-33. https://doi.org/10.36890/iejg.1062741.
EndNote Halbeısen L, Hungerbühler N, Läuchli J (October 1, 2022) Quadrilaterals as Geometric Loci. International Electronic Journal of Geometry 15 2 321–333.
IEEE L. Halbeısen, N. Hungerbühler, and J. Läuchli, “Quadrilaterals as Geometric Loci”, Int. Electron. J. Geom., vol. 15, no. 2, pp. 321–333, 2022, doi: 10.36890/iejg.1062741.
ISNAD Halbeısen, Lorenz et al. “Quadrilaterals As Geometric Loci”. International Electronic Journal of Geometry 15/2 (October 2022), 321-333. https://doi.org/10.36890/iejg.1062741.
JAMA Halbeısen L, Hungerbühler N, Läuchli J. Quadrilaterals as Geometric Loci. Int. Electron. J. Geom. 2022;15:321–333.
MLA Halbeısen, Lorenz et al. “Quadrilaterals As Geometric Loci”. International Electronic Journal of Geometry, vol. 15, no. 2, 2022, pp. 321-33, doi:10.36890/iejg.1062741.
Vancouver Halbeısen L, Hungerbühler N, Läuchli J. Quadrilaterals as Geometric Loci. Int. Electron. J. Geom. 2022;15(2):321-33.
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