纪录片《费马最后的定理》 第03期 勾股定理

（单词翻译）

Pierre de Fermat was a 17th-century French mathematician¹ who made some of the greatest breakthroughs in the history of numbers.

皮埃尔·德·费马是17世纪时期的法国数学家，他在数学历史上成就了一些最伟大的突破。

His inspiration came from studying the Arithmetica, that Ancient Greek text.

他的灵感来自于研习"算术"那本古希腊着作。

Fermat owned a copy of this book, which is a book about numbers with lots of problems, which presumably Fermat tried to solve.

费马有这本书的一份复本，这本书是关于数字以及许多难题，是费马力图解决的那些。

He studied it, he wrote notes in the margins².

他研习它，在空栏处写下笔记。

Fermat's original notes were lost, but they can still be read in a book published by his son.

费马的原始笔记已遗失，但在他儿子出版的书中可看到那些。

It was one of these notes that was Fermat's greatest legacy³.

这些笔记中的一条正是费马最伟大的遗产。

And this is the fantastic observation of Master Pierre de Fermat which caused all the trouble: "Cubum autem in duos cubos"

皮埃尔·德·费马大人的这个奇妙观察成果惹出了所有的麻烦："Cubum autem in duos cubos"。

This tiny note is the world's hardest mathematical problem.

这条短短的手记是世界上最困难的数学题。

It's been unsolved for centuries, yet it begins with an equation so simple that children know it off by heart.

数世纪以来未获破解，它起始于一个等式，简单得孩子们早已铭记于心。

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

直角三角形斜边的平方等于另两边平方之和。

Yes well that's Pythagoras's theorem isn't it, that's what we all did at school.

那就是勾股定理，不是吗，那正是我们在学校里都用过的。

So Pythagoras's theorem, the clever thing about it is that it tells us

对于勾股定理，其奇妙之处在于告诉了我们，

when three numbers are the sides of a right-angle triangle, that happens just when x squared plus y squared equals z squared.

当三个数字是个直角三角形的三条边时，x的平方+y的平方=z的平方时，就是那样。