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Dergiler / International Electronic Journal of Geometry / 2023 / Volume: 16 Issue: 2

The Pentagon Theorem in Miquelian Möbius Planes

Lorenz Halbeısen(ETH Zürich)0000-0001-6078-7237
Norbert Hungerbühler(ETH Zurich)0000-0001-6191-0022
Vanessa Loureiro(Realgymnasium Rämibühl Zürich)0009-0002-1999-5696
Sayfa
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Yayın Tarihi
2023-10-29
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition we identify five additional quintuples of points in the pentagon configuration which are concyclic.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We give an algebraic proof of the Pentagon Theorem.
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Temel Bulgular & Veri:The proof works in all Miquelian Möbius planes obtained from a separable quadratic field extension.
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Sonuç & Katkı:In addition we identify five additional quintuples of points in the pentagon configuration which are concyclic.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Pentagon theorem · Möbius planes · Miquel planes

Abstract

We give an algebraic proof of the Pentagon Theorem. The proof works in all Miquelian Möbius planes obtained from a separable quadratic field extension. In particular, the theorem holds in every finite Miquelian plane. The arguments also reveal that the five concyclic points in the Pentagon Theorem are either pairwise distinct or identical to one single point. In addition we identify five additional quintuples of points in the pentagon configuration which are concyclic.

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Bu Makaleye Atıf Yap

Halbeısen, L., Hungerbühler, N., Loureiro, V. (2023). The Pentagon Theorem in Miquelian Möbius Planes. International Electronic Journal of Geometry, Volume: 16 Issue: 2. https://doi.org/10.36890/iejg.1255469

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Kaynakça (7)

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  7. Miquel, A.: Théorèmes de géométrie. Journal de Mathématiques Pures et Appliquées. 3, 485–487 (1838).