{"title":"毕达哥拉斯三元组和爱森斯坦三元组的法雷和","authors":"M. Crasmareanu","doi":"10.36753/mathenot.1316554","DOIUrl":null,"url":null,"abstract":"A composition law, inspired by the Farey addition, is introduced on the set of Pythagorean triples. We study some of its properties as well as two symmetric matrices naturally associated to a given Pythagorean triple. Several examples are discussed, some of them involving the degenerated Pythagorean triple $(1, 0, 1)$. The case of Eisenstein triples is also presented.","PeriodicalId":489457,"journal":{"name":"Mathematical sciences and applications e-notes","volume":"95 23","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Farey sum of Pythagorean and Eisenstein triples\",\"authors\":\"M. Crasmareanu\",\"doi\":\"10.36753/mathenot.1316554\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A composition law, inspired by the Farey addition, is introduced on the set of Pythagorean triples. We study some of its properties as well as two symmetric matrices naturally associated to a given Pythagorean triple. Several examples are discussed, some of them involving the degenerated Pythagorean triple $(1, 0, 1)$. The case of Eisenstein triples is also presented.\",\"PeriodicalId\":489457,\"journal\":{\"name\":\"Mathematical sciences and applications e-notes\",\"volume\":\"95 23\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical sciences and applications e-notes\",\"FirstCategoryId\":\"0\",\"ListUrlMain\":\"https://doi.org/10.36753/mathenot.1316554\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical sciences and applications e-notes","FirstCategoryId":"0","ListUrlMain":"https://doi.org/10.36753/mathenot.1316554","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Farey sum of Pythagorean and Eisenstein triples
A composition law, inspired by the Farey addition, is introduced on the set of Pythagorean triples. We study some of its properties as well as two symmetric matrices naturally associated to a given Pythagorean triple. Several examples are discussed, some of them involving the degenerated Pythagorean triple $(1, 0, 1)$. The case of Eisenstein triples is also presented.
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