{"title":"球面和双曲双心多边形","authors":"Ren Guo","doi":"10.1007/s00010-024-01088-8","DOIUrl":null,"url":null,"abstract":"<p>Relations of circumradius, inradius and the distance between the circumcenter and incenter of Euclidean bicentric polygons are generalized into spherical geometry and hyperbolic geometry. The asymptotic behavior of these generalized formulas with small circumradius are studied. Relations for hyperbolic hyper-ideal bicentric polygons are derived.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Spherical and hyperbolic bicentric polygons\",\"authors\":\"Ren Guo\",\"doi\":\"10.1007/s00010-024-01088-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Relations of circumradius, inradius and the distance between the circumcenter and incenter of Euclidean bicentric polygons are generalized into spherical geometry and hyperbolic geometry. The asymptotic behavior of these generalized formulas with small circumradius are studied. Relations for hyperbolic hyper-ideal bicentric polygons are derived.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00010-024-01088-8\",\"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":"100","ListUrlMain":"https://doi.org/10.1007/s00010-024-01088-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Relations of circumradius, inradius and the distance between the circumcenter and incenter of Euclidean bicentric polygons are generalized into spherical geometry and hyperbolic geometry. The asymptotic behavior of these generalized formulas with small circumradius are studied. Relations for hyperbolic hyper-ideal bicentric polygons are derived.
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