That relationship can be derived from the Pythagorean theorem.

这种关系源于毕达哥拉斯定理。

One classic proof often attributed to Pythagoras himself uses a strategy called proof by rearrangement.

经典证明是毕达哥拉斯自己做出的，他利用了一种名叫排列的证明方法。

And it wasn't until 1945 that it was revealed to contain Pythagorean triples.

直到 1945 年，毕达哥拉斯三元组才被发。

Now, in modern times, we call this Pythagoras' theorem.

代，我们称之为毕达哥拉斯定理。

And I have tried to apprehend the Pythagorean power by which number holds away above the flux.

同时我还想理解毕达哥拉斯的力量，通过它的力量，驾驭了万物的变化。

Hippasus belonged to a group called the Pythagorean mathematicians who had a religious reverence for numbers.

希帕索是毕达哥拉斯学派中的一员他们对于字有着宗教般的崇敬。

In particular, the Mesopotamian understood Pythagorean triples at a level of sophistication that we never expected.

是美索不达米亚人对毕达哥拉斯三元组理解的复杂程度，是我们从未预料到的。

Pythagorus discovered that we were wrong.

毕达哥拉斯发我们错了。

And I have tried to comprehend the Pythagorean power by which number holds sway above the flux.

同时我还力图领悟毕达哥拉斯的力量，即字驾驭一切不稳定的强大力量。

Pythagoras was born the longest time ago in 570 B.C. and might have had the first laboratory ever recorded.

毕达哥拉斯出生于公元前570年，可能是有史以来第一个拥有有记载的实验室的人。

Empedocles thought he was a God and jumped into a volcano. And Pythagoras had an irrational fear of beans.

恩培多克勒以为他是天神，跳进了火山，毕达哥拉斯对豆子有莫名的恐惧。

The Pythagorean theorem has more than 350 proofs, and counting, ranging from brilliant to obscure.

毕达哥拉斯定理有超过 350 个证明，而且还增加，从聪明的到有些难懂的证明。

And it's actually a very old idea; it goes back over 2,000 years to Pythagoras.

这实际上是一个非常古老的想法；它可以追溯到 2000 多年前的毕达哥拉斯。

Scoots, I think you're thinking of tulip, not euclids, and Pythagoras.

斯库茨，我想你是想郁金香，而不是欧几里得和毕达哥拉斯。

Ancient philosophers, going back to Pythagoras, believed that your breath contained your soul.

追溯到毕达哥拉斯的古代哲学家相信你的呼吸包含你的灵魂。

And I want you to notice how well this lines up with the Pythagorean theorem.

我希望你注意到这与毕达哥拉斯定理有多吻合。

'It concealed the first principles of science in the calculations of Pythagoras.

“它毕达哥拉斯的计算中隐藏了科学的首要原则。

And Pythagoras had an irrational fear of beans.

毕达哥拉斯对豆子有莫名的恐惧。

Ooh. Pythagoras Buck.He's got the right angle.

天~毕达哥拉斯·巴克，他提出了这么的勾股定律。

When sir lawyer forsook thee, For Pythagore's sake, what body then took thee?

当律师先生为了毕达哥拉斯的缘故抛弃你时，是什么人带走了你呢？