{"title":"三角形的Zindler点","authors":"A. Berele, S. Catoiu","doi":"10.1080/0025570X.2022.2127301","DOIUrl":null,"url":null,"abstract":"Summary Zindler’s theorem of 1920 says that each planar convex set admits two perpendicular lines that divide it into four parts of equal area. Call the intersection of the two lines a Zindler point. We show that each triangle admits either one, two or three Zindler points, and we classify all triangles according to these three numbers.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Zindler Points of Triangles\",\"authors\":\"A. Berele, S. Catoiu\",\"doi\":\"10.1080/0025570X.2022.2127301\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary Zindler’s theorem of 1920 says that each planar convex set admits two perpendicular lines that divide it into four parts of equal area. Call the intersection of the two lines a Zindler point. We show that each triangle admits either one, two or three Zindler points, and we classify all triangles according to these three numbers.\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics Magazine\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0025570X.2022.2127301\",\"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.2022.2127301","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Summary Zindler’s theorem of 1920 says that each planar convex set admits two perpendicular lines that divide it into four parts of equal area. Call the intersection of the two lines a Zindler point. We show that each triangle admits either one, two or three Zindler points, and we classify all triangles according to these three numbers.
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