KaydedilenlerDerginizi ekleyin

Dergiler / International Electronic Journal of Geometry / 2021 / Volume: 14 Issue: 2

Reversion Porisms in Conics

Lorenz Halbeısen(ETH Zürich)0000-0001-6078-7237
Norbert Hungerbühler(ETH Zurich)0000-0001-6191-0022
Marco Schiltknecht(ETH Zürich)0000-0001-7381-2999
Sayfa
—
Yayın Tarihi
2021-10-29
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also investigate projective properties of the porisms.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri: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.
💡
Sonuç & Katkı:We also investigate projective properties of the porisms.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

🔖

Bu Makaleye Atıf Yap

Halbeısen, L., Hungerbühler, N., Schiltknecht, M. (2021). Reversion Porisms in Conics. International Electronic Journal of Geometry, Volume: 14 Issue: 2. https://doi.org/10.36890/iejg.979088

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (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).