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。

So, let's prove this theorem.

下面来证明这个定理。

So it is really the same theorem.

还是原来的的定理。

So, that's the divergence theorem.

这就是散度定理。

That was Greene's theorem.

旋度也出现了，那就是格林定理。

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 saw yesterday Green's theorem.

昨天讲了格林公式。

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。

OK, so this way is a fundamental theorem.

解决办法是基本定理。

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。

More complicated example Pythagoras's theorem.

在毕达哥拉斯定理中还有更复杂的例子。

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。

In the plane that is called Green's theorem.

平面上的就是格林公式。

Again, we have to use now the parallel axis theorem.

现在我们要用，平行移轴定理。

OK, and actually that's how we prove the theorem.

实际上，这也是我们证明的思路。

Did he do a handstand, solve the four-color map theorem?

他会倒立，解决这个四色地图原理？

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。

This is really one of the features of Green's theorem.

这是格林公式的一种表示。

Godel's incompleteness theorem seems like a practical joke.

哥德尔的不完全定理就象一个恶作剧。

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。

Well, remember in the case of work we had Green's theorem.

请记得做功的例子，可以用格林公式的。

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。