{"title":"与庞塞莱闭包定理有关的旋转指标","authors":"W. Cieslak, H. Martini, W. Mozgawa","doi":"10.1515/UMCSMATH-2015-0003","DOIUrl":null,"url":null,"abstract":"Let C R C r denote an annulus formed by two non-concentric circles C R , C r in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to C R C r , then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with C r , with n- gons for any n > k.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Rotation indices related to Poncelet’s closure theorem\",\"authors\":\"W. Cieslak, H. Martini, W. Mozgawa\",\"doi\":\"10.1515/UMCSMATH-2015-0003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let C R C r denote an annulus formed by two non-concentric circles C R , C r in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to C R C r , then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with C r , with n- gons for any n > k.\",\"PeriodicalId\":340819,\"journal\":{\"name\":\"Annales Umcs, Mathematica\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Umcs, Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/UMCSMATH-2015-0003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Umcs, Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/UMCSMATH-2015-0003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
摘要
设C R C R表示欧几里得平面上由两个非同心圆C R, C R组成的环。我们证明了如果Poncelet闭包定理对环切于ccr的k-gon成立，那么在这个环内存在满足Poncelet闭包定理和cr的圆，对于任意n- > k，有n- gon。
Rotation indices related to Poncelet’s closure theorem
Let C R C r denote an annulus formed by two non-concentric circles C R , C r in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to C R C r , then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with C r , with n- gons for any n > k.
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