{"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}
引用次数: 3
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.
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