He paused, surprised at the tears that sprang to Hagen's eyes.

He was so excited that tears started to his eyes.

他激动得热泪盈眶.

His prayer moved me to tears.

他的祈祷把我感动得热泪盈眶。

Researched Proposition on Pythagorean Theorem and Projection Theorem Analyzing the trends of proposition design on physical experiment in national college-entrance examinations

有关勾股定理、射影定理的研究性论题高考物理实验试题设计趋势分析

Legs of a Triangle Theorem and Chinese Ancient Mathematics

勾股定理与中国古代数学

The Pythagorean is not only the basis of some math theorems but also be widely used in life and production.

勾股定理不仅是一些数学定理的基础，在生产和生活中的应用也很广泛。

In this paper the linearly topological structure of Menger Probabilistic inner product space is discussed. In virtue of these, some more general convergence theorems, Pythagorean theorem, and the orthogonal projective theorem are established.

本文讨论了Menger概率内积空间的线性拓扑结构，建立了空间上较为一般的收敛定理，勾股定理及正交投影定理等。

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

By Combining both the Chines and western mathematical thinking, four new proof methods of Pythagorean theorem were demonstrated.

通过融合中西两种数学思想方法，给出了“勾股定理”的四种新的证明方法。

Cosine theorem and Pythagorean theorem in space

立体几何的余弦定理和勾股定理

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。

Using VBA Programming of PowerPoint to Make Exploration-and-Verification Interactive Courseware of Pythagorean Theorem

利用PowerPoint的VBA编程功能制作勾股定理的探索与验证交互性课件

View of Multi-culture on Right Angles Theorem

多元文化下的勾股定理

This paper discusses mang methods to prove Legs of a triangle and right angles theorem with cut area.

本文论述了用分割面积来证明勾股定理的多种方法。

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.

本文目的在于论述变换函数中φ，外延勾股定理用于运算任意三角形边的平方长并研究其几何特征的实际应用问题。

Area and Proof of Pythagorean Theorem~ α

面积与勾股定理的证明

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。

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 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。

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。

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。