{"title":"本科数学中的一个盲点:圆长度的定义，以及如何将其转化为一个有启发性的例子","authors":"A. Vernitski","doi":"10.21100/msor.v20i3.1300","DOIUrl":null,"url":null,"abstract":"We highlight the fact that in undergraduate calculus, the number pi is defined via the length of the circle, the length of the circle is defined as a certain value of an inverse trigonometric function, and this value is defined via pi, thus forming a circular definition. We present a way in which this error can be rectified. We explain that this error is instructive and can be used as an enlightening topic for discussing different approaches to mathematics with undergraduate students.","PeriodicalId":18932,"journal":{"name":"MSOR connections","volume":"38 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A blind spot in undergraduate mathematics: The circular definition of the length of the circle, and how it can be turned into an enlightening example\",\"authors\":\"A. Vernitski\",\"doi\":\"10.21100/msor.v20i3.1300\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We highlight the fact that in undergraduate calculus, the number pi is defined via the length of the circle, the length of the circle is defined as a certain value of an inverse trigonometric function, and this value is defined via pi, thus forming a circular definition. We present a way in which this error can be rectified. We explain that this error is instructive and can be used as an enlightening topic for discussing different approaches to mathematics with undergraduate students.\",\"PeriodicalId\":18932,\"journal\":{\"name\":\"MSOR connections\",\"volume\":\"38 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"MSOR connections\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21100/msor.v20i3.1300\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"MSOR connections","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21100/msor.v20i3.1300","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A blind spot in undergraduate mathematics: The circular definition of the length of the circle, and how it can be turned into an enlightening example
We highlight the fact that in undergraduate calculus, the number pi is defined via the length of the circle, the length of the circle is defined as a certain value of an inverse trigonometric function, and this value is defined via pi, thus forming a circular definition. We present a way in which this error can be rectified. We explain that this error is instructive and can be used as an enlightening topic for discussing different approaches to mathematics with undergraduate students.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
