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Year 2021, Volume: 14 Issue: 2, 371 - 382, 29.10.2021

Lorenz Halbeısen Norbert Hungerbühler Marco Schiltknecht

https://doi.org/10.36890/iejg.979088

Abstract

References

  • [1] Bogomolny, A.: The butterfly theorem. Interactive Mathematics Miscellany and Puzzles. http://www.cut-the-knot.org/pythagoras/Butterfly.shtml, accessed February 4, 2021.
  • [2] Coxeter, H. S. M., Greitzer, S. L.: Geometry revisited, volume 19 of New Mathematical Library. Random House, Inc. New York (1967).
  • [3] Izmestiev, I.: A porism for cyclic quadrilaterals, butterfly theorems, and hyperbolic geometry. Amer. Math. Monthly. 122 (5), 467–475 (2015).
  • [4] Jones, D.: Quadrangles, butterflies, Pascal’s hexagon, and projective fixed points. Amer. Math. Monthly. 87 (3), 197–200 (1980).
  • [5] Klamkin, M. S.: An Extension of the Butterfly Problem. Math. Mag. 38 (4), 206–208 (1965).
  • [6] Kocik, J.: A porism concerning cyclic quadrilaterals. Geometry, Article ID 483727: 5 pages (2013).
  • [7] Sliepčević, A.: A new generalization of the butterfly theorem. J. Geom. Graph. 6 (1), 61–68 (2002).
  • [8] Volenec, V.: A generalization of the butterfly theorem. Math. Commun. 5 (2), 157–160 (2000).

Reversion Porisms in Conics

Year 2021, Volume: 14 Issue: 2, 371 - 382, 29.10.2021

Lorenz Halbeısen Norbert Hungerbühler Marco Schiltknecht

https://doi.org/10.36890/iejg.979088

Abstract

We give a projective proof of the butterfly porism for cyclic quadrilaterals and present a general reversion porism for polygons with an arbitrary number of vertices on a conic. We also investigate projective properties of the porisms.

Keywords

Porisms butterfly theorems reversion map

References

  • [1] Bogomolny, A.: The butterfly theorem. Interactive Mathematics Miscellany and Puzzles. http://www.cut-the-knot.org/pythagoras/Butterfly.shtml, accessed February 4, 2021.
  • [2] Coxeter, H. S. M., Greitzer, S. L.: Geometry revisited, volume 19 of New Mathematical Library. Random House, Inc. New York (1967).
  • [3] Izmestiev, I.: A porism for cyclic quadrilaterals, butterfly theorems, and hyperbolic geometry. Amer. Math. Monthly. 122 (5), 467–475 (2015).
  • [4] Jones, D.: Quadrangles, butterflies, Pascal’s hexagon, and projective fixed points. Amer. Math. Monthly. 87 (3), 197–200 (1980).
  • [5] Klamkin, M. S.: An Extension of the Butterfly Problem. Math. Mag. 38 (4), 206–208 (1965).
  • [6] Kocik, J.: A porism concerning cyclic quadrilaterals. Geometry, Article ID 483727: 5 pages (2013).
  • [7] Sliepčević, A.: A new generalization of the butterfly theorem. J. Geom. Graph. 6 (1), 61–68 (2002).
  • [8] Volenec, V.: A generalization of the butterfly theorem. Math. Commun. 5 (2), 157–160 (2000).
There are 8 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

Marco Schiltknecht 0000-0001-7381-2999

Publication Date October 29, 2021
Acceptance Date October 5, 2021
Published in Issue Year 2021 Volume: 14 Issue: 2

Cite

APA Halbeısen, L., Hungerbühler, N., & Schiltknecht, M. (2021). Reversion Porisms in Conics. International Electronic Journal of Geometry, 14(2), 371-382. https://doi.org/10.36890/iejg.979088
AMA Halbeısen L, Hungerbühler N, Schiltknecht M. Reversion Porisms in Conics. Int. Electron. J. Geom. October 2021;14(2):371-382. doi:10.36890/iejg.979088
Chicago Halbeısen, Lorenz, Norbert Hungerbühler, and Marco Schiltknecht. “Reversion Porisms in Conics”. International Electronic Journal of Geometry 14, no. 2 (October 2021): 371-82. https://doi.org/10.36890/iejg.979088.
EndNote Halbeısen L, Hungerbühler N, Schiltknecht M (October 1, 2021) Reversion Porisms in Conics. International Electronic Journal of Geometry 14 2 371–382.
IEEE L. Halbeısen, N. Hungerbühler, and M. Schiltknecht, “Reversion Porisms in Conics”, Int. Electron. J. Geom., vol. 14, no. 2, pp. 371–382, 2021, doi: 10.36890/iejg.979088.
ISNAD Halbeısen, Lorenz et al. “Reversion Porisms in Conics”. International Electronic Journal of Geometry 14/2 (October 2021), 371-382. https://doi.org/10.36890/iejg.979088.
JAMA Halbeısen L, Hungerbühler N, Schiltknecht M. Reversion Porisms in Conics. Int. Electron. J. Geom. 2021;14:371–382.
MLA Halbeısen, Lorenz et al. “Reversion Porisms in Conics”. International Electronic Journal of Geometry, vol. 14, no. 2, 2021, pp. 371-82, doi:10.36890/iejg.979088.
Vancouver Halbeısen L, Hungerbühler N, Schiltknecht M. Reversion Porisms in Conics. Int. Electron. J. Geom. 2021;14(2):371-82.
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