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。
旋度也出现了，那就是格林定理。
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。
It s a very interesting theorem, says Brualdi.
“这是一个非常有趣的定理，”Brualdi说。
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 is Green for flux and that is the divergence theorem.
也就是通量的格林公式——散度公式。
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。
No? OK, so let's see, so how are we going to actually prove this theorem?
没有了吗？，来看看，到底应该怎么证明这个定理呢？
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。
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。
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？
The point is that Euclid's theorem is a lot more important than it initially looks.
重点在于勾股定理比看上去要重要得多。
It turns kinetic energy into heat, and that is perfectly fine in the work-energy theorem.
可以把动能转为热量，这点在功能定理，中是非常好的。
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。
For Dr Perelman, transforming a conjecture into a theorem appears to have been prize enough.
对于他而言，把猜想变为定理似乎要比变成奖金更能得到满足。
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, Green's theorem is another way to avoid calculating line integrals if we don't want to.
格林公式是另一种可以,避免计算线积分的方法。
The orientation that will work for this theorem is choosing the normal vector to point outwards.
对于这个定理，我选择的方向是,指向外的正方向。
So, these are special cases of what's called the fundamental theorem of calculus for line integrals.
这些都是反映了,线积分的微积分基本定理的特例。
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。
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