That relationship can be derived from the Pythagorean theorem.

这种关系源于毕达哥拉斯定理。

You might remember the Pythagorean theorem from school like what the formula is?

你可能还记得在学校学的勾股定理，比如公式是什么？

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，数驾驭了万物的变化。

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数字有着宗教般的崇敬。

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，即数字驾驭一切不稳定的强大力量。

It's like when I first encountered the Pythagorean Theorem.

就像我第一次接触勾股定理的感觉。

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，从聪明的到有些难懂的证明。

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。

And it turns out there's a variety of proofs of the Pythagorean Theorem.

其实有很多种证明勾股定理的方法。

The shape of the earth? The heliocentric universe? The Pythagorean theorem? The structure of DNA?

放弃对地球形状的认识？对以太阳为中心的宇宙的认识？还是对勾股定理的认识？对DNA结构的认识？

According to the converse of the Pythagorean theorem, that has to make a right triangle, and, therefore, a square corner.

根据毕达哥拉斯的逆定理，这就可以形成一个直角三角形，因此，便可形成直角。

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

特别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。

The Pythagorean “diatonic” scale, still the basis of most Western music, is made up from seven notes.

毕氏“全音阶”范围仍然是多数西方音乐的基石，它由七个音符组成。

Each blue outlined square contains the pieces of exactly one dark and one light gray square, proving the Pythagorean theorem again.

每个蓝色画出的正方形正好包含了一个深灰色正方形和一个浅灰色正方形，再次证明了毕达哥拉斯定理。

One of the most famous Pythagorean triples is 3,4,5,and that triangle is hiding all over your chessboard.

最著名的毕达哥拉斯三元组之一是 3、4、5，这个三角形隐藏在您的棋盘上。

So, the law of cosines is an extension of the pythagorean theorem to the arbitrary angles...

所以余弦定律是勾股定理对任意角度的延伸。

There are, in fact, points that are distance 5 from each other, which we know thanks to the Pythagorean Theorem.

事实上， 有些点彼此之间的距离为 5，这要归功于勾股定理。

He was hot on the French social systems, and talked of going to the Backwoods to found a sort of Pythagorean community.

他热衷于法国的社会制度， 并谈到去边远地区建立一种毕达哥拉斯社区。

They all came up with elegant proofs for the famous Pythagorean theorem; the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.

他们都对毕达哥拉斯定理（勾股定理）做出了精彩的证明；这个定理是说，对于一个直角三角形，一边的平方加上另一边的平方等于斜边的平方。

They all came up with elegant proofs for the famous Pythagorean theorem, the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.

他们都为著名的毕达哥拉斯定理提出了优雅的证明，这条规则说对于直角三角形，一侧的平方加上另一侧的平方等于斜边的平方。