莫雷五圆定理的隐藏孪生兄弟

Pub Date : 2023-10-20 DOI:10.1080/00029890.2023.2254179

Lorenz Halbeisen, Norbert Hungerbühler, Vanessa Loureiro

{"title":"莫雷五圆定理的隐藏孪生兄弟","authors":"Lorenz Halbeisen, Norbert Hungerbühler, Vanessa Loureiro","doi":"10.1080/00029890.2023.2254179","DOIUrl":null,"url":null,"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.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Hidden Twin of Morley’s Five Circles Theorem\",\"authors\":\"Lorenz Halbeisen, Norbert Hungerbühler, Vanessa Loureiro\",\"doi\":\"10.1080/00029890.2023.2254179\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-10-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/00029890.2023.2254179\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00029890.2023.2254179","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

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。

查看原文

微信好友朋友圈 QQ好友复制链接

The Hidden Twin of Morley’s Five Circles Theorem

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助