{"title":"矩形，曲线和克莱因瓶","authors":"R. Schwartz","doi":"10.1090/bull/1755","DOIUrl":null,"url":null,"abstract":"In this article I will survey some results about inscribing triangles and quadrilaterals in Jordan curves. I will focus on the recent result of Josh Greene and Andrew Lobb, which says that for any smooth embedded loop C and any aspect ratio λ, there are four points in C which make the vertices of a rectangle of aspect ratio λ.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Rectangles, curves, and Klein bottles\",\"authors\":\"R. Schwartz\",\"doi\":\"10.1090/bull/1755\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article I will survey some results about inscribing triangles and quadrilaterals in Jordan curves. I will focus on the recent result of Josh Greene and Andrew Lobb, which says that for any smooth embedded loop C and any aspect ratio λ, there are four points in C which make the vertices of a rectangle of aspect ratio λ.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2021-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/bull/1755\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/bull/1755","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
In this article I will survey some results about inscribing triangles and quadrilaterals in Jordan curves. I will focus on the recent result of Josh Greene and Andrew Lobb, which says that for any smooth embedded loop C and any aspect ratio λ, there are four points in C which make the vertices of a rectangle of aspect ratio λ.
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