a2=b2+cd, an Extended Pythagorean Formula

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-07-17 DOI:10.1080/00029890.2023.2231798

F. Laudano

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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a2=b2+cd，勾股公式的一个推广

亨利·佩里格尔是一位业余数学家，1868年至1897年为伦敦数学学会会员。他最出名的可能是通过解剖和换位来证明勾股定理[3，4]。在这里，我们扩展了Perigal方法，为一个被称为扩展毕达哥拉斯公式[1，2]的结果给出了一个新的证明。考虑三角形ABC，其中BC≥AB。设D为AC上的点，使得BD=AB，E为BA的扩展上的点（其中AE=DC）。三角形EAA′和CDB是全等的，EA′=CB，A EA′=D CB。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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