{"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":9513,"journal":{"name":"Bulletin of the American Mathematical Society","volume":" ","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/bull/1755","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
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.
期刊介绍：
The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.
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