查询词典 analytical geometry

On a stage of discussing the virtual teaching reform, a new graphics education system among the Institutions of Technology has been being built up and perfected. The author demonstrated how to evaluate the position where descriptive geometry is and what function descriptive geometry plays when it comes to the changing graphics education system. The author also discussed how to use descriptive geometry to cultivate students' thinking and design capacity.

摘 要：在探讨实质性教学改革阶段，工科院校新的图学教学体系正在不断改进和完善，怎样看待画法几何课程在这个体系中的位置、价值和功能，如何利用画法几何来培养学生的思维能力和设计能力，是否认为CAD技术与画法几何没有必然联系。

For example, teaching outline about research on elementary geometry must be redesigned, teaching plan and courses system should also be revised. Particularly, the course 揜esearch on elementary geometry and Higher geometry?

初等几何研究"课程的教学大纲需要重新制订，其课程体系和教学内容也需要大幅度调整，特别是将原来的"初等几何研究"课程和"高等几何"课程合并成为一门课程，并将该课程的教学目的从初等几何"研究转到初等几何教学素质的培养上来。

More specifically, Gauss studied the geometry of surfaces based on the first fundamental form (also called "line element") of surfaces and generalized Euclidean geometry to "curved geometry" on surfaces.

局部微分几何的一个里程碑是 Gauss关于曲面的理论，他建立了基于曲面第一基本形式的几何，并把欧几里得几何推广到曲面上"弯曲"的几何。

In the fourth chapter, I analyze and contrast many architectural cases in history and modern times which ellipse were applied to, and explore the ellipse"s development in historic sense. The fifth chapter investigates the dynamic relationship between geometry and architecture based on ellipse"s geometric character, and analyzes ellipse architecture"s characters in symbolism, dualism, diversity and unity these four facets. In the sixthchapter, taking ellipse architecture as examples, I try to explore the relationship between the more general geometry"s purity and architecture"s complexity, and build the foundation for future exploration of geometry"s purity.

第四章从历史和现代两个方面展开了大量对椭圆形式在建筑中应用的个案和实例的研究与对比，探讨了椭圆形式在历史上意义的变迁；第五章以椭圆的几何特性为立足点，研究了椭圆几何--建筑之间的动态关系，从标志性，二元对立，多样和统一四个方面分析了椭圆建筑的特点；第六章以椭圆建筑为例，尝试探讨了更一般的几何的纯粹性与建筑的复杂性的关系，对几何纯粹性意义的挖掘为进一步的研究提供基础；第七章采用了类型对比的研究方法，分析了安藤忠雄和库哈斯两位设计哲学截然不同的建筑师对椭圆形式的使用；另外，以位置关系为线索，将椭圆和其他的几何形式结合起来，总结了一般情况下几何的纯粹性对建筑复杂性的作用。

The vector has the rich actual background and the widespread application function, it has the algebra and the geometry dual statuses, causes the algebra geometrization, the geometry algebra, has communicated the algebra, the geometry and the trigonometric function, has the good analysis method and the complete structure.

向量具有丰富的实际背景和广泛的应用功能，它具有代数和几何双重身份，使代数几何化、几何代数化，沟通了代数、几何与三角函数，具有良好的分析方法和完整的结构。

The theorems of Ibn al-Haytham, Omar Khayyam and Nasir al-Din al-Tusi on quadrilaterals , including the Lambert quadrilateral and Saccheri quadrilateral , were the first theorems on elliptical geometry and hyperbolic geometry , and along with their alternative postulates, such as Playfair's axiom , these works had a considerable influence on the development of non-Euclidean geometry among later European geometers, including Witelo , Levi ben Gerson , Alfonso , John Wallis , and Giovanni Girolamo Saccheri .

定理伊本Haytham，欧玛尔海亚姆和纳西尔基地丁铝土司上quadrilaterals ，包括德兰伯特四边形和萨凯里四边形，是第一个椭圆形的几何定理和双曲几何，并连同其替代假设，如普莱费尔的公理，这些作品有相当发展的影响非欧几里德几何之间稍后欧洲geometers ，包括Witelo ，列维本格森，阿方索，约翰瓦利斯和乔瓦吉罗拉莫萨凯里。

Results A view of better understanding origins of Gaussian intrinsic differential geometry is presented,and the intrinsic relation between Gauss′s thought of intrinsic differential geometry and of his non-Euclidean geometry is brought to light and discussed.

结果 总结分析了高斯建立的内蕴微分几何的思想和渊源，揭示了其与非欧几何学的内在联系。

In chapter 4, some vector mathematical definitions are first given to position tolerance zones; second, the principle of variation geometry is introduced, and the mathematical foundation of automatic generation of a approximate linear equation of tolerance design function by variation geometry is first proven; tangent method and two-point slope method based variation geometry are main studied.

第四章首先对一些位置公差带给出了矢量化的数学定义；然后介绍了变动几何的原理，首次论证了变动几何能产生近似线性公差设计函数的数学依据，并着重研究了基于变动几何的切线法和二点斜率法。

In this thesis,the AM1,MNDO,MINDO/3(mainly AM1)and INDO/S-CI semiempirical MO methods were used toinvestigate the excited-state intramolecular protontransfer reactions of salicylic acid derivatives—salicylic acid,methyl salicylate,salicylaldehyde,o-hydroxyaceto-phenone,salicylamide and 3-hydroxy-picolinamide (6 conformers and 2-3 anion species);2-(2'-hydroxy-5' methylphenyl) benzotriazole(4 conformers),2-(2' hydroxyphenyl) benzimidazole (3 conformers and 3anion species),Bis-2,5-(2-benzoxazolyl)hydroquinone(3 conformers),2-(2'-hydroxyphenyl)benzothiazole(2conformers) and 7-azaindole dimer (2 conformers).Theinvestigations were described as follows.Geometry optimization,relative stability andhydrogen bonding energy First,for sylicylic acid derivative molecules,the AM1,MNDO and MINDO/3 methods were used toinvestigate ground-state geometry optimization,energies,relative stabilities and hydrogen-bondingenergies on the five kinds of the molecules(designing 6 conformers and 2-3 anion species).Comparing with experimental data,the optimizedgeometry,the order of stability,the hydrogen-bonding energies and the distances between O-O in O-H..O hydrogen bonds by AM1 method were in agreementwith the experimental data,however,the C-C bondlengths optimized by MNDO and MINDO/3 were longer,C-O and O-H bond lengths were shorter;for C-N bondlengths,the results opitimized by MNDO method werethe same as those by AM1 method,nevertheless the C-Nbond lengths given by MINDO/3 method were muchshorter.For some sylicylic acid derivatives(e.g.methyl salicylate,salicylamide),the order ofstabilities on the conformers given by MNDO andMINDO/3 methods were not in agreement with theexisting conformers deduced by experimental methods,and the hydrogen bonding energies calculated by MNDO.and MINDO/3 methods were smaller.Second,the studyon the other systems found that the optimizedgeometry of the proton-transfered product with INDOmethod could not be obtained,only could theoptimized geometry of reactant be obtained,and thecalculated hydrogen bonding energies were greater.Many results of calculation indicated that the studyon the excited-state intramolecular proton transferreaction system using AM1 method was suitable andreliable.

本论文用AM1、MNDO、MINDO/3（主要是AM1）和INDO/S-CI半经验分子轨道方法对水杨酸衍生物系列——水杨酸、水杨酸甲酯、水杨醛、O-羟基乙酰苯酮、水杨酰胺和3-羟基吡啶酰胺（6种异构体和2-3种阴离子）；2-（2'-羟基-5'-甲基苯基）苯并三〓唑（4种异构体）；2-（2'-羟基苯基）苯并咪唑（3种异构体和3种阴离子）；2，5-二间氮杂氧茚氢醌（3种异构体）；2-（2'-羟基苯基）间〓杂硫茚（2种异构体）和7-〓吲哚二体（2种异构体）的激发态分子内质子转移反应在以下几个方面进行了较系统的理论研究：几何构型优化和相对稳定性及氢键能首先以水杨酸衍生物系列分子为例，用AM1、MNDO和MINDO/3方法考察了5种分子（每种分子设计6种异构体和2-3种阴离子）的基态几何构型优化，能量、相对稳定性和氢键能计算，通过和实验数据进行比较，AM1方法给出的优化几何构型、稳定性次序、氢键能和O—H。。。O氢键的0—0距离与实验数据吻合最好，MNDO和MINDO/3方法优化的C-C键长偏长，C-O键和O-H键长偏短；对于C-N键长，MNDO和AM1优化结果差别不大，而MINDO/3给出了过短的C-N键长，MNDO和MINDO/3方法给出的有些水杨酸衍生物分子（如水杨酸甲酯和水杨酰胺）异构体的稳定性次序和实验上推测的可存在异构体结果不一致，MNDO和MINDO/3方法给出的氢键能偏低，对其他体系的研究发现INDO方法常常不能得到质子转移产物的优化几何构型，只能得到反应物的优化构型，并且估算的氢键能偏高，大量的计算结果表明AM1方法对本论文研究的激发态分子内质子转移反应体系是适宜和可靠的。

The crystal structures have been determined by single-crystal X-ray diffraction.Cadmium atoms in compounds 1 and 2 show an eight-coordinated distorted square-antiprismatic geometry and a seven-coordinated distorted pentagonal bipyramidal geometryrespectively. Copper atoms in compounds 3 and 4 show a six-coordinated distorted threeprismatic geometry and a four-coordinated distorted tetrahedral geometry respectively.

所有配合物的晶体结构都通过单晶X-射线衍射确定：配合物1中的镉离子周围显示八配位的扭曲四方反棱柱构型；而配合物2中的镉离子周围显示七配位的扭曲五角双锥构型；配合物3中的铜离子周围显示六配位的扭曲三棱柱构型；配合物4中的铜离子周围显示四配位的扭曲四面体构型；配合物5中的锌离子周围显示六配位的扭曲八面体构型。

You can do some assertiveness training.

你可以进行一些自信训练。

We were well on the path to making a rear-wheel-drive global platform," says Mays."

我们正致力于建立一个后轮驱动的平台，"Mays这样说道。"