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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 2

Reversion Porisms in Conics

NORBERT HUNGERBÜHLER
LORENZ HALBEISEN
MARCO SCHILTKNECHT
Pages
371–382
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also investigate projective properties of the porisms.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:We also investigate projective properties of the porisms.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Porisms · butterfly theorems · reversion map

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.

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Cite This Article

HUNGERBÜHLER, N., HALBEISEN, L., SCHILTKNECHT, M. (2022). Reversion Porisms in Conics. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 2, 371–382. https://ajindex.com/articles/539569

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References (8)

  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).