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？

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。

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。

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。

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？

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。

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。

I began to study trigonometry. There was solace in its strange formulas and equations. I was drawn to the Pythagorean theorem and its promise of a universal—the ability to predict the nature of any three points containing a right angle, anywhere, always.

我开始学习三角学。奇怪的公式和方程让人安心。我被勾股定理及其通用性深深吸引——它始终能预测任意一个直角三角形三边的关系。