{"title":"等边三角形的迭代过程得到恒等式1/3+1/9+1/27+…=1/2","authors":"Levi L. Bicua, Precious R. Tayaben, A. Racca","doi":"10.35974/ISC.V6I1.1207","DOIUrl":null,"url":null,"abstract":"In this paper, we define a particular iterative process and apply it to triangles. It was shown that the process results to self-similar triangles if and only if the generator triangle is an equilateral triangle. Furthermore, the identity 1/3+1/9+1/27+...=1/2 resulted from the process.","PeriodicalId":7363,"journal":{"name":"Abstract Proceedings International Scholars Conference","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Iterative Process Applied to Equilateral Triangles Resulting to the Identity 1/3+1/9+1/27+…=1/2.\",\"authors\":\"Levi L. Bicua, Precious R. Tayaben, A. Racca\",\"doi\":\"10.35974/ISC.V6I1.1207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we define a particular iterative process and apply it to triangles. It was shown that the process results to self-similar triangles if and only if the generator triangle is an equilateral triangle. Furthermore, the identity 1/3+1/9+1/27+...=1/2 resulted from the process.\",\"PeriodicalId\":7363,\"journal\":{\"name\":\"Abstract Proceedings International Scholars Conference\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abstract Proceedings International Scholars Conference\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.35974/ISC.V6I1.1207\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abstract Proceedings International Scholars Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35974/ISC.V6I1.1207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Iterative Process Applied to Equilateral Triangles Resulting to the Identity 1/3+1/9+1/27+…=1/2.
In this paper, we define a particular iterative process and apply it to triangles. It was shown that the process results to self-similar triangles if and only if the generator triangle is an equilateral triangle. Furthermore, the identity 1/3+1/9+1/27+...=1/2 resulted from the process.
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