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.
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.
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。
给出了函数形式的单调类定理的几种推广形式。
Some generalizing forms for monotone class theorems of functional forms are given.
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.
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.
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.
弱化了刘维尔定理的条件，给出了刘维尔定理的一个推广。
This paper weakened the Liouville s theorem conditions, and gives the Liouville theorem of a promotion.
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.
分析了最小熵产生定理的适用范围和它与非平衡定态稳定性的关系。
The theorem of minimum entropy production and its implication to stability of nonequilibrium stationary states are examined.
从这种机器理论数学的角度上讲，就是有没有证明数学定理的算法。
In mathematical terms, they wanted to know whether there was an algorithm for proving the theorems of mathematics.
与此同时，实现了一些数学(群论)定理的机器证明，命题的逻辑推演等。
At the same time implemented machine proof of some mathematical theorems (Group theory) and logical Inference of statements.
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.”
基于塑性力学上限定理的土压力计算，在数值上可以通过单元集成法来实现。
Earth pressure calculation based on upper bound theorem of plasticity can be numerically performed by element integration method.
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.
早期的人工智能研究集中在了一些看起来很困难的智力活动上，如高水平国际象棋，或者积分定理的证明。
Early A.I. research concentrated on what seemed to be difficult intellectual tasks, such as playing grandmaster level chess, or proving theorems in integral calculus.
早期的人工智能研究集中在了一些看起来很困难的智力活动上，如高水平国际象棋，或者积分定理的证明。
Early A.I. research concentrated on what seemed to be difficult intellectual tasks, such as playing grandmaster level chess, or proving theorems in integral calculus.
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