This article introduces the whole course of the demonstrating device of the Pythagorean theorem with the glass plate.

The Pythagorean Theorem tells us that a3-4-5 triangle is a right triangle, so we can simply test for sides of3,4, and5.

勾股定理（Pythagorean Theorem）告诉我们边长为3、4和5的三角形是直角三角形，因此可以使用边长3、4和5来简单地测试。

For instance, it's also the square of the Euclidean norm on R2, the length of a two-dimensional vector, a part of the triangle inequality, and quite a bit more.

例如，R2的平方、二维向量的长度、三角不等式等都存在勾股定理。

In all my years I have never once attended a cocktail party where the conversation turned to the Pythagorean theorem.

活了这些年，我还从来没有介入过一场谈判勾股定理的鸡尾酒会。

Different nations step into the reacher about The Pythagorean at different times.

对勾股定理的研究，不同民族在起始时间上不同。

He even came up on his own with a way to prove the Pythagorean theory.

甚至相出了一个自己的方法来证明勾股定理。

And we learned how to prove the Pythagorean Theorem in Euclidean geometry, starting with the various axioms in Euclidean geometry, ba, ba-ba, ba-ba, ba-ba, ba bum.

我们都学习过，欧几里得几何中对勾股定理的证明方法，从繁杂的欧氏几何的公理开始，邦，邦邦，邦邦，邦邦。

If our predecessors understood the hadith the way some of us try to understand it, they would have never produced the great scholars who invented algorithms and developed trigonometry.

如果我们的前辈以我们有些人试着理解的方式来理解这段圣训，他们绝对不会出现发明运算法则和揭示勾股定理的伟大学者。

Generalized Pythagorean Theorem in n-dimensional Euclidean Space

关于n维欧氏空间上的广义勾股定理

One New Study for First Proving of the "Pythagorean Theorem"

勾股定理最早证明新考

The Transformation and General Pythagoras' Theorem on the Linear Manifold

线性流型上的变换函数Φ及广义的勾股定理

When leaders treat the member well occasionally , they accept any and all crumbs gratefully.

当领导者偶尔略施小惠, 他们便感激涕零.

The eagerness in the author's voice told him that he had guessed right.

作家声音里流露出来的感激涕零的急切语气使他明白:他是猜对了.

When I have nothing, the love of God and His grace overwhelm me!

当我没了一切, 神的爱与恩典浇灌令我感激涕零!

It is as often applied to feelings which arise from an half-hour's acquaintance.

这通常总是用来形容男女一见钟情.

Both were stuck at the same moment.

俩人一见钟情.

The Cornwall coast was a pitiful sight to behold.

康沃尔一带海岸让人触景生情,十分惋惜.

Well, I have mixed emotions.

哎, 真是百感交集.

He read these things with mingled feelings.

他百感交集地读着这些消息.

Boss : My feelings are mixed on the issue too.

我也百感交集.

He could never see the face of Goldstein without a painful mixture of emotions.

每次看到戈德斯坦的面孔,他都禁不住百感交集,痛苦异常.