欧拉不等式的另一个证明

Q4 Mathematics

Mathematics Magazine Pub Date : 2023-10-20 DOI:10.1080/0025570x.2023.2266332

Nam Gu Heo

{"title":"欧拉不等式的另一个证明","authors":"Nam Gu Heo","doi":"10.1080/0025570x.2023.2266332","DOIUrl":null,"url":null,"abstract":"SummaryEuler’s inequality in Euclidean geometry is a famous result relating the circumradius and inradius of a triangle. We provide a new proof of this result using elementary ideas about area and isosceles triangles.MSC: 51M04 Additional informationNotes on contributorsNam Gu HeoNAM GU HEO (MR Author ID: 1106949) studied mathematics education and received an Ed.D. from the Korea National University of Education. Currently, he is a professor at Sunchon National University, Korea.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Another Proof of Euler’s Inequality\",\"authors\":\"Nam Gu Heo\",\"doi\":\"10.1080/0025570x.2023.2266332\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SummaryEuler’s inequality in Euclidean geometry is a famous result relating the circumradius and inradius of a triangle. We provide a new proof of this result using elementary ideas about area and isosceles triangles.MSC: 51M04 Additional informationNotes on contributorsNam Gu HeoNAM GU HEO (MR Author ID: 1106949) studied mathematics education and received an Ed.D. from the Korea National University of Education. Currently, he is a professor at Sunchon National University, Korea.\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-20\",\"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.2023.2266332\",\"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.2023.2266332","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: 0

摘要

欧几里得几何中的乌勒不等式是关于三角形的外半径和内半径的一个著名结果。我们利用面积和等腰三角形的初等思想，给出了一个新的证明。顾贺南(作者编号:1106949)，数学教育专业，获教育学博士学位。来自韩国国立教育大学。目前，他是韩国顺天国立大学的教授。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Another Proof of Euler’s Inequality

SummaryEuler’s inequality in Euclidean geometry is a famous result relating the circumradius and inradius of a triangle. We provide a new proof of this result using elementary ideas about area and isosceles triangles.MSC: 51M04 Additional informationNotes on contributorsNam Gu HeoNAM GU HEO (MR Author ID: 1106949) studied mathematics education and received an Ed.D. from the Korea National University of Education. Currently, he is a professor at Sunchon National University, Korea.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematics Magazine Mathematics-Mathematics (all)

CiteScore

0.20

自引率

0.00%

发文量