The Hidden Twin of Morley’s Five Circles Theorem

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-10-20 DOI:10.1080/00029890.2023.2254179

Lorenz Halbeisen, Norbert Hungerbühler, Vanessa Loureiro

引用次数: 0

Abstract

We give an algebraic proof of a slightly extended version of Morley’s Five Circles Theorem. The theorem holds in all Miquelian Möbius planes obtained from a separable quadratic field extension, in particular in the classical real Möbius plane. Moreover, the calculations bring to light a hidden twin of the Five Circles Theorem that seems to have been overlooked until now.

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莫雷五圆定理的隐藏孪生兄弟

给出了莫雷五圆定理的一个稍微扩展的代数证明。该定理适用于所有由可分离二次域扩展得到的密克尔平面Möbius，特别是经典实数平面Möbius。此外，这些计算还揭示了五圈定理的一个隐藏的孪生兄弟，这个孪生兄弟迄今为止似乎一直被忽视。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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