这里我们再看看一个关于此定理的论点。
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.
文中还讨论了结构变更定理的若干应用。
Some applications of the theorem are also discussed in the paper.
完成了该定理的初等证明。
我将讲述一些，关于Stokes定理的曲面独立性。
So, I'm going to say a couple of words about surface independence in Stokes theorem.
完整的分析必须建立在隐函数定理的基础上。
A complete analysis must build on the implicit function theorem.
摘要给出了线性代数中几个定理的矩阵证法。
Matrix proofs of several theorems in linear algebra are given.
同时，牛顿-莱布尼兹定理的条件可以改进。
另外，我们给出一个定理的一种不同的证明。
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.
讨论具有某种特征映射的类似柯西积分定理的结论。
A discussion on some characterized mapping conclusions similar to Cauchy integral theorem.
本文介绍了柯西中值定理的多种证明方法及其应用。
This paper introduces the proof and application of Cauchy mean-value theorem from many angles in every aspect.
公布一个程序的源代码与公布一个定理的证明是一样的。
Publishing the source code of a program is the equivalent of publishing the proof of a theorem.
理论上说，存在排除某些人使用某句诗歌或某个数学定理的可能。
It is theoretically possible to exclude some from the use of a poem, or a mathematical theorem, but exclusion is generally quite difficult.
本文表明关于KKM定理的某些最近的结果是错误的。
In this paper, we show that some recent results on KKM theorem are false.
布置的作业是作一个可以用于证明毕达哥拉斯定理的图。
The assignment was to make a construction that could be used in proving the pythagorean theorem.
作为其应用，我们给出了素模型存在定理的另一种证明。
As its application, we give a new proof of the existence theorem of prime models.
但是对于这个，我需要找到一个可以运用Stokes定理的曲面。
But for that, I needed to be able to find a surface which to apply Stokes theorem.
我们甚至没有讲过它,当我们运用机械能,守恒定理的时候。
We didn't even talk about it when we did the conservation of mechanical energy.
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, that's the end of the proof. OK, so you see, the idea is really the same as for Green's theorem.
由于这个定理的使用条件是非常清楚的，从而分析了一些矛盾。
The clarity of the theorem's service conditions results in the analysis of a few contradictions.
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。”
The sensation of working on a theorem, he says, can be like being “a hunter and gatherer of mathematical concepts.”
本文以数学定理的形式指出该体系具有一类新的决定论的、物理内容明显的结果。
In this paper we point out in the form of mathematical theorem that the system possesses new and deterministic results with evident physical meanings.
自然地，如果你们上过8。,可能已经看到，散度定理的应用,在诸如力场、电场上的应用。
Now, of course, 02 if you're doing 8.02, then you might actually have seen the divergence theorem already being used for things that are more like force fields, say, electric fields and so on.
给出柯西中值定理的一个新的证法，说明柯西中值定理也可由拉格朗日中值定理导出。
This paper gives the new method to prove the cauchy mean value theorem which also may be deduced from the Lagrange mean value theorem.
其他的章节是关于巴赫的赋格曲和伟大的德国数学家Kurt Gordel的定理的。
Other chapters are focused on Bach's fugues and the theorems of great German mathematician Kurt Gordel.
从安德鲁·怀尔斯对费马大定理的解答中获得的理解比费马大定理给出的原始信息更深刻。
The solution of this conjecture by Andrew Wiles provided an understanding of this structure uncomparably deeper than the original message carried by the Fermat Theorem.
在数学里，一旦一个定理的证明被公布了，就不需要一个权利机构去认证这个定理是成立的。
In mathematics, once the proof of a theorem is published, there is no need for any authority to certify that the theorem is true.
如果定理的条件被证明为真，则我们可以使用此定理来确定我们的程序的定理结果的正确性。
If the conditions of the theorems are shown to be true, then we can use the theorem to establish the truth of the theorem's result for our program.
如果定理的条件被证明为真，则我们可以使用此定理来确定我们的程序的定理结果的正确性。
If the conditions of the theorems are shown to be true, then we can use the theorem to establish the truth of the theorem's result for our program.
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