The primary aim of this paper is to describe the transformation function [ 1], to extend the conclusion of Pythagoras'theorem for "squared length" of any triangle and to study some geometrical significance of its application.

Area and Proof of Pythagorean Theorem~ α

面积与勾股定理的证明

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The general expressions in integer of the Pythagorean Theorem have infinite equivalent forms.

勾股定理（即毕达格拉斯定理）的全部整数解表达式有无穷多种，目前常用的勾股定理全部整数解表达式，不过是其中最简通解式而已。

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A proof on the Pythagorean theorem in n-dimension vector space

n维空间中勾股定理的一个证明

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The Pythagorean is one of the greatest theorems we can express it simply that if the triangle is an right triangle, then square its two angled-sides and plus them, the summation equals to the square of the hypotenuse.

勾股定理是世界上最伟大的定理之一，其简单表述为：直角三角形两直角边的平方和等于斜边的平方。

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In this paper, firstly we assure that Ancient China and Ancient Greece found out the theorem simultaneously, according to investigating its origin and history, the principle and Ancient Found Priority judging criteria.

本文通过研究勾股定理的的起源和历史，根据古代发现优先权的确立原则与判定标准确定了古希腊和古代中国同时发现了勾股定理这一结论。

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It is generally considered that the Greece mathematician, Pythagoras, first proved the Pythagorean theorem, but this is not reliable.

在西方，一般都认为：希腊数学家半达哥拉斯（Pythagoras）最早证明了勾股定理，因而都习惯地称这个定理为毕达哥拉斯定理。但这一看法历史上并没有可靠的依据。

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Even if admit this view, in the western countries the time of first proof of the Pythagoras theorem is not probably early than epoch ago 585 year.

即使承认这一看法，西方最早给出勾股定理证明的时间也不会早于公元前585年，即相传毕达哥拉斯出生的那一年。

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This article introduces the whole course of the demonstrating device of the Pythagorean theorem with the glass plate.

介绍了用玻璃板制作勾股定理演示器的全过程。

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The Pythagorean Theorem tells us that a3-4-5 triangle is a right triangle, so we can simply test for sides of3,4, and5.

勾股定理（Pythagorean Theorem）告诉我们边长为3、4和5的三角形是直角三角形，因此可以使用边长3、4和5来简单地测试。

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For instance, it's also the square of the Euclidean norm on R2, the length of a two-dimensional vector, a part of the triangle inequality, and quite a bit more.

例如，R2的平方、二维向量的长度、三角不等式等都存在勾股定理。

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In all my years I have never once attended a cocktail party where the conversation turned to the Pythagorean theorem.

活了这些年，我还从来没有介入过一场谈判勾股定理的鸡尾酒会。

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Different nations step into the reacher about The Pythagorean at different times.

对勾股定理的研究，不同民族在起始时间上不同。

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He even came up on his own with a way to prove the Pythagorean theory.

甚至相出了一个自己的方法来证明勾股定理。

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And we learned how to prove the Pythagorean Theorem in Euclidean geometry, starting with the various axioms in Euclidean geometry, ba, ba-ba, ba-ba, ba-ba, ba bum.

我们都学习过，欧几里得几何中对勾股定理的证明方法，从繁杂的欧氏几何的公理开始，邦，邦邦，邦邦，邦邦。

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If our predecessors understood the hadith the way some of us try to understand it, they would have never produced the great scholars who invented algorithms and developed trigonometry.

如果我们的前辈以我们有些人试着理解的方式来理解这段圣训，他们绝对不会出现发明运算法则和揭示勾股定理的伟大学者。

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Generalized Pythagorean Theorem in n-dimensional Euclidean Space

关于n维欧氏空间上的广义勾股定理

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One New Study for First Proving of the "Pythagorean Theorem"

勾股定理最早证明新考

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The Transformation and General Pythagoras' Theorem on the Linear Manifold

线性流型上的变换函数Φ及广义的勾股定理

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When leaders treat the member well occasionally , they accept any and all crumbs gratefully.

当领导者偶尔略施小惠, 他们便感激涕零.

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The eagerness in the author's voice told him that he had guessed right.

作家声音里流露出来的感激涕零的急切语气使他明白:他是猜对了.

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