That relationship can be derived from the Pythagorean theorem.

这种关系源于毕达哥拉斯定理。

Pythagorus discovered that we were wrong.

毕达哥拉斯发现我们错了。

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

在现代，我们称之为毕达哥拉斯定理。

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现。

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，用了一种名叫排列证明方法。

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

希帕是毕达哥拉斯学派中一员们对于数字有教般崇敬。

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力量，通过它力量，数驾驭了万物变化。

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力量，即数字驾驭一切不稳定强大力量。

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

恩培多克勒以为是天神，跳进了火山，毕达哥拉斯对豆子有莫名恐惧。

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

特别是美不达米亚人对毕达哥拉斯三元组理解复杂程度，是我们从未预料到。

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实验室人。

And Pythagoras had an irrational fear of beans.

毕达哥拉斯对豆子有莫名恐惧。

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.

“它在毕达哥拉斯计算中隐藏了科学首要原则。

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，而且还在增加，从聪明到有些难懂证明。

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

追溯到毕达哥拉斯古代哲学家相信你呼吸包含你灵魂。

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

天~毕达哥拉斯·巴克，提出了这么勾股定律。

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

斯库茨，我想你是在想郁金香，而不是欧几里得和毕达哥拉斯。

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想法；它可以追溯到 2000 多年前毕达哥拉斯。

It is the old Pythagorean Theorem we learned in our first geometry class.

这是我们在第一堂几何课上学到古老毕达哥拉斯定理。