信息论用数学精度捕获噪声影响的定理概括了这一思想。
Information theory generalises this idea via theorems that capture the effects of noise with mathematical precision.
我把我成功的大部分原因归结于学习数学的收获，尤其是分析复杂原则的那些定理。
I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles.
我们可以把斯图尔特定理直接应用于三角形的中线上。
We can apply Stewart's theorem directly to the median of a triangle.
有时被称为,经典的能量均分定理。
Sometimes it's called the classical equipartition of energy theorem.
那么散度定理究竟讲的是什么？
现在我们要用，平行移轴定理。
旋度也出现了，那就是格林定理。
著名的定理决定数学的风景。
有些程序可以证明数学定理。
如前所述，证明以公理和定理做为其论据。
As I mentioned before, proofs use axioms and theorems to make their case.
为什么定理选择逆时针积分而不是顺时针呢？
Why does the theorem choose counterclockwise over clockwise?
他们能保持对社会的既定理念吗？
Can they preserve their static conception of their societies?
其实有很多种证明勾股定理的方法。
And it turns out there's a variety of proofs of the Pythagorean Theorem.
这就是散度定理。
那就是散度定理。
重点在于勾股定理比看上去要重要得多。
The point is that Euclid's theorem is a lot more important than it initially looks.
对于这个定理，我选择的方向是,指向外的正方向。
The orientation that will work for this theorem is choosing the normal vector to point outwards.
这些都是反映了,线积分的微积分基本定理的特例。
So, these are special cases of what's called the fundamental theorem of calculus for line integrals.
“这是一个非常有趣的定理，”Brualdi说。
“这是一个非常有趣的定理，”Brualdi说。
我相信，机械能守恒定理，我忽略了张力。
I believed in the conservation of mechanical energy and I overlooked the tension.
该领域充满了美妙的定理，等待着人们去采撷和整理。
The terrain was strewn with beautiful theorems begging to be picked up and arranged in unified order.
没有了吗？，来看看，到底应该怎么证明这个定理呢？
No? OK, so let's see, so how are we going to actually prove this theorem?
可以把动能转为热量，这点在功能定理，中是非常好的。
It turns kinetic energy into heat, and that is perfectly fine in the work-energy theorem.
在散度定理中的约定是,将曲面的定向取为外法线的方向。
The convention in the divergence theorem is that we orient the surface with a normal vector pointing always outwards.
会得到完全相同的答案，我觉得用功能定理，会更加的简洁。
You get exactly the same result, and I find this somehow more pleasing to use the work-energy theorem.
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。
For Dr Perelman, transforming a conjecture into a theorem appears to have been prize enough.
定理是基本的原理，我们可以将其组合起来以获得更多的成果。
Theorems are fundamental truths that can be combined to more easily achieve further results.
这边是空间上的，这边是平面上的，我们来看看关于做功的定理。
This side will be space, this side will be the plane and we are going to start with theorems about work.
定理（theorems）由公理推论得到的关于程序的陈述。
theorems which are statements about the program inferred from the axioms.
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