{"title":"双曲线内的整数序列和椭圆链","authors":"H. Belbachir, L. Németh, Soumeya Merwa Tebtoub","doi":"10.33039/ami.2020.06.002","DOIUrl":null,"url":null,"abstract":"We propose an extension to the work of Lucca [Giovanni Lucca, Integer sequences and circle chains inside a hyperbola, Forum Geometricorum , Vol-ume 19. 2019, 11–16]. Our goal is to examine chains of ellipses inside a hyperbola, and we derive recurrence relations of centers and minor (major) axes of the ellipse chains. We also determine conditions for these recurrence sequences to consist of integer numbers.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"31 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Integer sequences and ellipse chains inside a hyperbola\",\"authors\":\"H. Belbachir, L. Németh, Soumeya Merwa Tebtoub\",\"doi\":\"10.33039/ami.2020.06.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose an extension to the work of Lucca [Giovanni Lucca, Integer sequences and circle chains inside a hyperbola, Forum Geometricorum , Vol-ume 19. 2019, 11–16]. Our goal is to examine chains of ellipses inside a hyperbola, and we derive recurrence relations of centers and minor (major) axes of the ellipse chains. We also determine conditions for these recurrence sequences to consist of integer numbers.\",\"PeriodicalId\":43454,\"journal\":{\"name\":\"Annales Mathematicae et Informaticae\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Mathematicae et Informaticae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33039/ami.2020.06.002\",\"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":"Annales Mathematicae et Informaticae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33039/ami.2020.06.002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Integer sequences and ellipse chains inside a hyperbola
We propose an extension to the work of Lucca [Giovanni Lucca, Integer sequences and circle chains inside a hyperbola, Forum Geometricorum , Vol-ume 19. 2019, 11–16]. Our goal is to examine chains of ellipses inside a hyperbola, and we derive recurrence relations of centers and minor (major) axes of the ellipse chains. We also determine conditions for these recurrence sequences to consist of integer numbers.
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