{"title":"真实的数字","authors":"Daniel W. Cunningham","doi":"10.2307/j.ctv14163vk.6","DOIUrl":null,"url":null,"abstract":"0. In their constructions, the Egyptians use the rational approximation for the irrational π ≈ 22 7 number. π ≈ 3 141592. ...... a. What is the relative error of their approximation? 1. Consider the number. 3 a. Carefully explain the meaning of the number to an elementary school student: 3 is the number that 3 b. Using a compass and straightedge only, give a formal construction of (a segment with length) 3 c. Using pencil and paper only, approximate the decimal value of by bisection 3 (interval halving). Show all intermediate results.","PeriodicalId":262028,"journal":{"name":"Real Analysis: With Proof Strategies","volume":"105 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Real Numbers\",\"authors\":\"Daniel W. Cunningham\",\"doi\":\"10.2307/j.ctv14163vk.6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"0. In their constructions, the Egyptians use the rational approximation for the irrational π ≈ 22 7 number. π ≈ 3 141592. ...... a. What is the relative error of their approximation? 1. Consider the number. 3 a. Carefully explain the meaning of the number to an elementary school student: 3 is the number that 3 b. Using a compass and straightedge only, give a formal construction of (a segment with length) 3 c. Using pencil and paper only, approximate the decimal value of by bisection 3 (interval halving). Show all intermediate results.\",\"PeriodicalId\":262028,\"journal\":{\"name\":\"Real Analysis: With Proof Strategies\",\"volume\":\"105 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Real Analysis: With Proof Strategies\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2307/j.ctv14163vk.6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Real Analysis: With Proof Strategies","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2307/j.ctv14163vk.6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
0. In their constructions, the Egyptians use the rational approximation for the irrational π ≈ 22 7 number. π ≈ 3 141592. ...... a. What is the relative error of their approximation? 1. Consider the number. 3 a. Carefully explain the meaning of the number to an elementary school student: 3 is the number that 3 b. Using a compass and straightedge only, give a formal construction of (a segment with length) 3 c. Using pencil and paper only, approximate the decimal value of by bisection 3 (interval halving). Show all intermediate results.
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