{"title":"a2=b2+cd, an Extended Pythagorean Formula","authors":"F. Laudano","doi":"10.1080/00029890.2023.2231798","DOIUrl":null,"url":null,"abstract":"Henry Perigal was an amateur mathematician and a member of the London Mathematical Society from 1868 to 1897. He is perhaps best known for his proof of the Pythagorean theorem by dissection and transposition [3, 4]. Here we extend the Perigal method to give a new proof for a result that has been called the extended Pythagorean formula [1, 2]. Consider triangle ABC, with BC ≥ AB. Let D be the point on AC such that BD = AB and E the point on the extension of BA where AE = DC. The triangles EAA′ and CDB are congruent, EA′ = CB, and A EA′ = D CB.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Mathematical Monthly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00029890.2023.2231798","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Henry Perigal was an amateur mathematician and a member of the London Mathematical Society from 1868 to 1897. He is perhaps best known for his proof of the Pythagorean theorem by dissection and transposition [3, 4]. Here we extend the Perigal method to give a new proof for a result that has been called the extended Pythagorean formula [1, 2]. Consider triangle ABC, with BC ≥ AB. Let D be the point on AC such that BD = AB and E the point on the extension of BA where AE = DC. The triangles EAA′ and CDB are congruent, EA′ = CB, and A EA′ = D CB.
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