解析几何

After getting these four line-of-sight vectors, we inverse these data in special observation coordinate based on space analytical geometry, then we can get the vector that has three components on every coordinate, this vector will be treated as the total wind profile in the three-dimensional observation field, the result of this four-point method can basically reflect all the spatial and temporal variation of the atmospheric wind.

在得到视线方向风速矢量后，从选定的三维观测坐标系对这四个矢量进行空间解析几何的运算，可得到观测坐标系的各坐标轴上四个测量矢量的各坐标分量的标量和。从而以这个在三个坐标轴上都有分量的矢量作为在观测视场内的总的风场的风速矢量。

In the CAD system for progressive dies, the method is introduced to automatically generate geometric models of stampings through inputting the product drawings by AutoCAD and picking-up the entity information from DXF files and programming with ObjectARX and C＋＋ language, at the same time, generating algorithm of close contour lines and unidirectional chain-table structure are used to express the models of stampings, the class and direct judgment of contour lines are realized and the entity existing side is judged by analytical geometry, which efficiently solves the problem of automatic input of drawings of stamping and providing information of process planning and mold design.

在级进模CAD系统中，将产品的图形信息以AutoCAD直接绘图形式输入到计算机中，从AutoCAD的图形交换文件中提取信息，采用面向对象的二次开发工具ObjectARX和C＋＋语言编写接口程序，并通过封闭轮廓的生成算法自动生成冲裁零件的几何模型，且用单向链表的形式加以表达，同时对冲裁零件图形的轮廓进行分类与走向判定，采用简单的解析几何方法对实体存在侧进行判定，有效地实现了零件图形的自动输入，为级进模CAD系统的工艺计算和模具工作部分的设计等提供了必要的信息。

English Description It aim at: developing comprehension of algebra, trigonometry, analytical geometry, derivation and integral, activating capabilities of logic inference and induction, enlightening confidence and independence, strengthening calculating abilities with an emphasis on its application and graph, furnishing a sound basis for future specialty.

Chinese Description 本课程希望在二学年中，能使学生对代数、三角、解析几何、微分及积分有充分的了解、培养逻辑推理、启发思考创造、强化计算演绎并注重应用与作图，以建立同学未来学习工程数学及相关专业课程之数学基础，充分达到学以致用的目的。

MathCAD ; analytical geometry ; FRAME ; animate ; programme

MathCAD ；解析几何；帧变量；动画；编程

As we all known, with the founding of Euclidean geometry in ancient Greece, with the development of analytic geometry and other kinds of geometries, with F.Kline" s Erlanger program in 1872 and the new developments of geometry in 20th century such as topology and so on, man has developed their understand of geometry. On the other hand, Euclid formed geometry as a deductive system by using axiomatic theory for the first time. The content and method of geometry have dramatically changed, but the geometry curriculum has not changed correspondingly until the first strike from Kline and Perry" s appealing.

纵观几何学发展的历史，可以称得上波澜壮阔：一方面，从古希腊时代的欧氏综合几何，到近代解析几何等多种几何的发展，以及用变换的方法处理几何的埃尔朗根纲领，到20世纪拓扑学、高维空间理论等几何学的新发展，这一切都在不断丰富人们对几何学的认识；另一方面，从欧几里得第一次使用公理化方法把几何学组织成一个逻辑演绎体系，到罗巴切夫斯基非欧几何的发现，以及希尔伯特形式公理体系的建立，极大地发展了公理化思想方法，不管是几何学的内容还是方法都发生了质的飞跃。

We shall have occasion to deal with geometry, both Euclidean and non-Euclidean, with arithmetic, algebra, analytic geometry, the theory of irrationals, set-theory, calculus of probability, and mathematical logic.

我们将与算术，代数，解析几何机会几何处理，包括欧几里德和非欧几里德，是无理的理论，集理论，概率演算，和数学逻辑。

And a basic understanding of Cartesian geometry, too.

和一些理解解析几何的知识。

By analytic geometry method and solving quadratic equation,a computer simulation algorithm of digital projection under arbitrary scanning locus was proposed.The algorithm is based on the rules of attenuation of monochromatic X-rays.Through mathematical modeling and computer simulation,digital projections of ellipsoid and cylinder in circular and helix scanning modes are exemplified respectively,which are proved to be correct by FDK and PI-line reconstruction algorithms.

介绍了一种利用解析几何和求解二次方程仿真任意扫描轨迹下的锥束射线投影数据算法，该方法基于单色射线贯穿物体的衰减理论，通过数学建模与计算机仿真，给出了椭球、圆柱两种典型模型分别在单圆、螺旋线扫描轨迹下的投影数据仿真结果，并利用FDK和PI线重建算法进行验证，证明了该种数值仿真方法的正确性。

"Closed curve, one of the conic sections of analytic geometry, consisting of all points whose distances from each of two fixed points add up to the same value."

解析几何中圆锥截线的一条封闭曲线，包含了与两个定点之距离呈等值增加的所有点。

This curriculum primary coverage includes: Function and limit, a circular function derivative and differential, theorem of mean and derivative application, indefinite integral, definite integral, definite integral application, space analytic geometry and vector algebra, function of many variables differential method and application, multiple integral, curvilinear integral and surface integral, infinite series, differential equation.

该课程的主要内容有：函数与极限，一元函数的导数与微分，中值定理与导数的应用，不定积分，定积分，定积分的应用，空间解析几何和向量代数，多元函数微分法及其应用，重积分，曲线积分与曲面积分，无穷级数，微分方程。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失