We can apply Stewart's theorem directly to the median of a triangle.
我们可以把斯图尔特定理直接应用于三角形的中线上。
So, that's the divergence theorem.
这就是散度定理。
So, what does the divergence theorem say?
那么散度定理究竟讲的是什么？
And that is called the divergence theorem.
那就是散度定理。
There are mathematical theorem-proving programs.
有些程序可以证明数学定理。
"It's a very interesting theorem," says Brualdi.
“这是一个非常有趣的定理，”Brualdi说。
Again, we have to use now the parallel axis theorem.
现在我们要用，平行移轴定理。
The No Free Lunch theorem and the importance of bias
NFL原理（原文为NoFreeLunch theorem，即没有免费的午餐定理）和倾向的重要性
The rate of sampling, related to the Nyquist theorem.
抽样的频率，这与奈奎斯原理有关。
Why does the theorem choose counterclockwise over clockwise?
为什么定理选择逆时针积分而不是顺时针呢？
That's a closed curve. So, I would like to use Green's theorem.
这是封闭曲线，所以我们可以用格林公式。
Sometimes it's called the classical equipartition of energy theorem.
有时被称为,经典的能量均分定理。
All I have to do is apply my mind. - There's no theorem, no proof.
我所需要做的只是使用我的大脑。-这没有定律，也没有证明。
But, you can't use Green's theorem directly if the curve is not closed.
但是，如果曲线不是封闭的，不能直接使用格林公式。
To "prove the theorem" means to show that the implication is a tautology.
“证明这个定理”就是要证明这个蕴涵式是一个重言式。
So, that's by the divergence theorem using the fact that s is a closed surface.
所以那是通过散度定理得到的，其中使用了S是封闭曲面这一事实。
OK, so the other thing I wanted to say is, what does this theorem say physically?
另一件事是，这个定理在物理学上有什么含义？
So, I'm going to say a couple of words about surface independence in Stokes theorem.
我将讲述一些，关于Stokes定理的曲面独立性。
So, there's one place in real life where Green's theorem used to be extremely useful.
现实生活中有一个方面，格林公式曾经非常有用。
So, there is an extended version of Green's theorem that tells you the following thing.
于是，就有格林公式的推广，它描述了如下内容。
Well, to be able to use Stokes theorem, I need, actually, to find a surface to apply it to.
为了能够应用Stokes定理，我需要找一个曲面来应用它。
Publishing the source code of a program is the equivalent of publishing the proof of a theorem.
公布一个程序的源代码与公布一个定理的证明是一样的。
So, using Green's theorem, the way we'll do it is I will, instead, compute a double integral.
那么，使用格林公式，我们去计算二重积分。
So, that's the end of the proof. OK, so you see, the idea is really the same as for Green's theorem.
这就是最终的证明了，证明的思路和证明格林定理的是一样的。
So, the divergence theorem gives us a way to compute the flux of a vector field for a closed surface.
散度定理为我们提供了一种，计算向量场通过闭曲面的通量的方法。
You get exactly the same result, and I find this somehow more pleasing to use the work-energy theorem.
会得到完全相同的答案，我觉得用功能定理，会更加的简洁。
It is true, and the proof comes as an application of a fixed point theorem which I discussed a year ago.
这是真的，证据来自不动点原理的一种运用，一年前我曾探讨过它。
Look up words and concepts like abacus, Thales’ theorem, obtuse triangle and a lot more in this special site.
Math Glossary:这里可以查找像算盘、泰勒斯定理，钝角三角形等等更多的单词以及概念。
Pythagoras is best known for the theorem that bears his name, but it was discovered much earlier in Mesopotamia.
毕达哥拉斯最出名的是与他同名的定理，不过这一定理在美索不达米亚更早被人们发现。
The sensation of working on a theorem, he says, can be like being “a hunter and gatherer of mathematical concepts.”
他说，专注于一个定理的感觉，就像“一个猎人，一个数学概念的收集者。”
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