论文部分内容阅读
早在公元前一世纪前,我国就有一部古书——《周髀算经》。书中说,西周初年商高讲过“勾三股四弦五”,这说明我国很早就知道了勾股定理。勾股定理用式子表示即a~2+b~2=c~2。通常把a、b、c叫做一组勾股数。古希腊数学家刁番都曾以m+2mn~(1/2)、n+2mn~(1/2)、m+n+2mn~(1/2)来找勾股数(其中m、n为正整数,2mn是一个完全平方数)。我国清代数学家罗士琳也提出m~2-n~2、2mn、m~2+n~2是一组勾股数(m、n为正整数,且m>n)。我对一些勾股数组观察后,初步归纳出以正整数a(a≥3)来寻找b、c的方法:
As early as in the 1st century BC, there was an ancient book in our country, Zhouyi Sutra. The book says that in the early days of the Western Zhou Dynasty, Shang Gao had talked about “hook three shares of four strings and five,” which shows that China knew the Pythagorean Theorem very early. The Pythagorean theorem is expressed by the formula a~2+b~2=c~2. Usually a, b, c are called a group of the number of shares. The ancient Greek mathematician Zhai Fandu used m+2mn~(1/2), n+2mn~(1/2), and m+n+2mn~(1/2) to find the number of hooks (m,n Is a positive integer, 2mn is a complete square number). Luo Shilin, a mathematician in the Qing Dynasty in China, also proposed that m~2-n~2,2mn and m~2+n~2 are a group of numbers of hooks (m and n are positive integers and m>n). After observing some of the Pythagorean arrays, I initially summarized a method for finding b and c with a positive integer a (a≥3):