the Pythagorean theorem

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

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。

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。

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

勾股定理最早证明新考

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。

Make the Demonstrating Device of the Pythagorean Theorem with the Glass Plate

用玻璃板制作勾股定理演示器

Context: The Pythagorean Theorem was proved using deductive reasoning.

上下文：毕德哥拉斯定理被人们运用演绎推理加以了证明。

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。

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。

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。

The teaching case that the Pythagorean theorem that this text offers proves is the application of probing into teaching.

本文提供的勾股定理证明的教学案例就是一次探究性教学的应用。