{"title":"对基本三角不等式的新认识","authors":"Martin Lukarevski","doi":"10.1080/0025570X.2023.2176106","DOIUrl":null,"url":null,"abstract":"Summary We give a simple proof of the fundamental inequality of the triangle based on calculation of the cosine of an angle in one particular triangle formed from familiar centers. For the term which appears in the inequality we give a bound as a rational expression in terms of and . Then as an application we derive new refinements of Gerretsen’s and Kooi’s inequalities.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A New Look at the Fundamental Triangle Inequality\",\"authors\":\"Martin Lukarevski\",\"doi\":\"10.1080/0025570X.2023.2176106\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary We give a simple proof of the fundamental inequality of the triangle based on calculation of the cosine of an angle in one particular triangle formed from familiar centers. For the term which appears in the inequality we give a bound as a rational expression in terms of and . Then as an application we derive new refinements of Gerretsen’s and Kooi’s inequalities.\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-02-15\",\"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.2023.2176106\",\"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.2023.2176106","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Summary We give a simple proof of the fundamental inequality of the triangle based on calculation of the cosine of an angle in one particular triangle formed from familiar centers. For the term which appears in the inequality we give a bound as a rational expression in terms of and . Then as an application we derive new refinements of Gerretsen’s and Kooi’s inequalities.
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