平面几何

In Chapter 5, in geometric perspectives, the geometric properties of complex numbers are explored, including complex plane, four arithmetic operations of complex numbers and nth root of a complex number. It is also exemplified how these geometric properties are applied to solving the problems of plane geometry.

第五章从几何的观点探索复数的几何性质，包括复数平面、复数的四则运算及复数的n次方根，并举出几个例子，说明这些几何性质如何应用在解决平面几何的问题上。

It was a little book on Euclidean plane geometry.

那是一本有关欧几里德平面几何的小册子。

At the age of 12 I experienced a second wonder of a totally different nature: in a little book dealing with Euclidean plane geometry, which came into my hands at the beginning of a school year.

在我12岁时，我经历了另一种性质完全不同的惊奇：这是在一个学年开始时，当我得到一本关于欧几里得平面几何的小书时所经历的。

In Euclidean plane geometry terms, being a parallelogram is : affine transformations always take one parallelogram to another one.

用欧氏平面几何术语，平行就是：仿射变换总是将一个平行四边形变成另一个平行四边形。

The first modestly skillful full-board chess program; the first checkers program, which defeated a regional champion; a program able to prove theorems in Euclidean plane geometry, which could pass the problem-solving section of a New York State high school regents examination; and serious research in both speech and character recognition were all part of the IBM Research playbook.

第一款水平一般的全棋盘象棋程序；第一款跳棋程序，它打败了区跳棋冠军；能证明欧几里德平面几何定理的程序，它能通过纽约高中入学考试；还有对语言和字符识别上的重要研究；这些都是IBM研究部打的算盘。

The non-commutativity of two gen-erators in an algebra or a group can usually lead to a certain geometrical phase.whose magnitude is generally an area of a circuit(e.g.a triangle)in a certain space.such as the spherical surface or the Euclidean plane.

通常一个群或且一个代数中两个生成元的不对易性会导致某种几何相位。这种相位可能对应于球面或且欧几里德平面几何中某个闭合回路的面积。

The merits of the invention is: it uses virtual instrument to realize function adjusting and extending; realizes flat geometry parameter normalization evaluation in continuous light, aids with analysis of fuzzy moving image, realizes the quick measurement of sports character, and it has no limit to the frequency; it uses image matching technology to realize the high precise sport character test in flash light.

本发明的优点在于：采用虚拟仪器方式实现功能调整和扩展；在连续光照明下，实现平面几何量参数的归一化评定，辅以模糊运动图像的分析，实现运动特性的快速测量，且对频率无限制；在频闪照明下，利用图像匹配技术实现高精度的运动特性测试。

Any object having a shape similar to a plane geometric figure with four equal sides and four right angles.

一个外形近似于平面几何中的正方形的物体，即有四个相同的边和四个直角。

The Application of Graphic Solution in Industrial Design;2. A graphic solution to ensuring the protection range of lightning rod is put forward instead of the complicated formulas,and the methods are discussed of the protection zone of single lightning rod,double and four lightning rods.

针对避雷针设计过程中计算公式过于复杂的问题，提出了利用平面几何作图求解避雷针联合保护范围的方法，给出了单支、双支和四支避雷针保护范围的作图解题步骤，并利用计算机图形仿真，给出了避雷针保护范围的空间结构图形。

A graphic solution to ensuring the protection range of lightning rod is put forward instead of the complicated formulas,and the methods are discussed of the protection zone of single lightning rod,double and four lightning rods.

针对避雷针设计过程中计算公式过于复杂的问题，提出了利用平面几何作图求解避雷针联合保护范围的方法，给出了单支、双支和四支避雷针保护范围的作图解题步骤，并利用计算机图形仿真，给出了避雷针保护范围的空间结构图形。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了