{"title":"闭次摆线和表摆线的分类","authors":"Zarema S. Seidametova, V. Temnenko","doi":"10.1080/0025570X.2023.2167397","DOIUrl":null,"url":null,"abstract":"Summary The paper describes a classification of closed epicycloids and hypocycloids into three classes: “odd/odd,” “even/odd,” “odd/even.” A subset of “perfect” epicycloids and hypocycloids that do not have self-intersection points has been identified. A new composite geometric object is constructed: the Euler Ring of Rings, consisting of a perfect epicycloid and a perfect hypocycloid with the same indices.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Classification of Closed Hypocycloids and Epicycloids\",\"authors\":\"Zarema S. Seidametova, V. Temnenko\",\"doi\":\"10.1080/0025570X.2023.2167397\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary The paper describes a classification of closed epicycloids and hypocycloids into three classes: “odd/odd,” “even/odd,” “odd/even.” A subset of “perfect” epicycloids and hypocycloids that do not have self-intersection points has been identified. A new composite geometric object is constructed: the Euler Ring of Rings, consisting of a perfect epicycloid and a perfect hypocycloid with the same indices.\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics Magazine\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0025570X.2023.2167397\",\"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":"Mathematics Magazine","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0025570X.2023.2167397","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
A Classification of Closed Hypocycloids and Epicycloids
Summary The paper describes a classification of closed epicycloids and hypocycloids into three classes: “odd/odd,” “even/odd,” “odd/even.” A subset of “perfect” epicycloids and hypocycloids that do not have self-intersection points has been identified. A new composite geometric object is constructed: the Euler Ring of Rings, consisting of a perfect epicycloid and a perfect hypocycloid with the same indices.
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