{"title":"扩展双曲空间中线段的中点坐标","authors":"L. Romakina","doi":"10.36890/iejg.1270550","DOIUrl":null,"url":null,"abstract":"In this article, we find an analytical characteristic of the type of a line and derive the formulae for calculating the coordinates of the midpoints and quasi-midpoints of elliptic, hyperbolic, and parabolic segments in an extended hyperbolic space $H^3$ in the frame of the first type. The space $H^3$ we consider in the Cayley\\,--\\,Klein projective model as a projective three-dimensional space with an oval quadric $\\gamma$ fixed in it.","PeriodicalId":43768,"journal":{"name":"International Electronic Journal of Geometry","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Coordinates of the Midpoint of a Segment in an Extended Hyperbolic Space\",\"authors\":\"L. Romakina\",\"doi\":\"10.36890/iejg.1270550\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we find an analytical characteristic of the type of a line and derive the formulae for calculating the coordinates of the midpoints and quasi-midpoints of elliptic, hyperbolic, and parabolic segments in an extended hyperbolic space $H^3$ in the frame of the first type. The space $H^3$ we consider in the Cayley\\\\,--\\\\,Klein projective model as a projective three-dimensional space with an oval quadric $\\\\gamma$ fixed in it.\",\"PeriodicalId\":43768,\"journal\":{\"name\":\"International Electronic Journal of Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Electronic Journal of Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.36890/iejg.1270550\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.36890/iejg.1270550","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Coordinates of the Midpoint of a Segment in an Extended Hyperbolic Space
In this article, we find an analytical characteristic of the type of a line and derive the formulae for calculating the coordinates of the midpoints and quasi-midpoints of elliptic, hyperbolic, and parabolic segments in an extended hyperbolic space $H^3$ in the frame of the first type. The space $H^3$ we consider in the Cayley\,--\,Klein projective model as a projective three-dimensional space with an oval quadric $\gamma$ fixed in it.
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