The theorem that alternativity can replace associativity is true.
交替性可以代替关联性的定理是正确的。
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。
下面来证明这个定理。
So, that's the divergence theorem.
这就是散度定理。
We saw yesterday Green's theorem.
昨天讲了格林公式。
We just use the fundamental theorem.
只需要应用基本定理就行。
Here is an argument for this theorem.
这里我们再看看一个关于此定理的论点。
We can just use the fundamental theorem.
仅需应用基本定理。
So, what does the divergence theorem say?
那么散度定理究竟讲的是什么？
If you want, in a way, it's this theorem.
可以这样想，这就是定理告诉我们的。
And that is called the divergence theorem.
那就是散度定理。
Why is this not like conceptually a new theorem?
为什么这个看上去不是一个新的定理呢？
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。
OK, and actually that's how we prove the theorem.
实际上，这也是我们证明的思路。
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
And for each of them, you will apply Green's theorem.
对于它们中的每一个，使用格林公式。
The rate of sampling, related to the Nyquist theorem.
抽样的频率，这与奈奎斯原理有关。
This is really one of the features of Green's theorem.
这是格林公式的一种表示。
We have a connection between that, which is Stokes theorem.
还有一种联系的方式就是Stokes定理。
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？
At that part is actually math, namely, the divergence theorem.
那部分是数学的东西，即散度定理。
So, we've seen the statement of Green's theorem in two forms.
我们已经了解了，格林公式的两种表达形式。
Well, that's the statement of the theorem we are trying to prove.
这就是我们试图证明的定理。
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。
One is direct calculation, and the other one is Green's theorem.
一种是直接计算，另一种则是格林公式。
Sometimes it's called the classical equipartition of energy theorem.
有时被称为,经典的能量均分定理。
Now, let's instead try to use Stokes' theorem to do the calculation.
现在使用Stokes定理来算。
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