抛物面

He believes the form he is holding is a hyperbolic paraboloid, a shape well known to mathematicians - or something very close to that - but he wants to be able to prove this conjecture.

他相信他手中的摺纸形式是一种数学家所熟知的双曲线抛物面，或是某种非常接近的形式，於是他想要验证此推测。

The authors show that the hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces.

作者证实：单叶双曲面和双曲抛物面是直线曲面。

On the basis of these theories, The specific project—the hyperbolic paraboloid shell structure named Shijingshan Gymnasium is introduced, and the finite element model is established, including calculation of load, simplification of node nature and simplification of support.

在这些理论的基础上，引入工程实例——石景山体育馆双曲抛物面网壳结构，建立有限元模型，包括使用荷载的计算、节点性质的简化、支承的简化等。

We discover that under a general configuration the twist system of this mechanism belongs to the seventh special three-system, and all the twist axes are distributed on a hyperbolic paraboloid that is special and unusual and rarely studied. Under original configuration it belongs to the fourth special three-system.

我们发现：该机器人在一般位形下，它的所有运动螺旋轴线在空间分布的二次曲面是比较特殊的，罕见的，是过去理论上研究很少的双曲抛物面，属于第七种特殊三系，在起始位置时属于第四种的特殊三系。

The main research contents are stated asfollow: 1. Simplified analysis method of space grids structuresDouble-layer space grids have been assumed as sandwich plate, and are analyzed bythe nontraditional theory of plate with consideration of shear deformation and threegeneralized displacements. Using the theory of energy variation, simplified methodsfor bending, stability and vibration analysis of double-layer space grids have been putforward based upon the idea of split rigidity. The formulas for calculating internalforces, displacements, critical load and natural frequency have been given out. Set thestable cables and bearing cables in hyperbolic paraboloid cable nets are all replaced bytruss-cable to form truss-cable nets structures. Natural vibration analysis method fortruss-cable nets structures has been put forward using the energy variation method andRayleigh method.

主要内容包括： 1、空间网格结构静动力简化分析方法把网架结构简化为夹层板，采用考虑剪切变形的具有三个广义位移的平板弯曲理论进行分析，基于分解刚度思想利用能量变分原理提出了网架结构弯曲、稳定与振动分析的简化计算方法，给出了位移、内力、屈曲临界荷载和固有频率的计算公式；将双曲抛物面索网中的稳定索与承重索均用劲性索代替形成劲性索网结构，基于能量变分法和Rayleigh法给出了劲性索网结构固有振动分析的简化计算公式。

Analyses of loci in the π plane and meridian line s show that the parabolic and hyperbolic type failure envelopes have no influences on the shape of the.

对改进式所作的π平面极限线和子午线分析表明，采用抛物线和双曲线形强度包络线基本上不会改变原准则在π平面上的极限线形状，但子午线由直线改为曲线，极限面在主应力空间内分别为抛物面和双曲面，其锥顶距坐标原点也比采用线性强度包络线的要小。

The primary reflector and the secondary reflector of the double-reflecting optical converging primary system are paraboloidal and hyperbolical mirrors, respectively.

所述双反射光学会聚主系统的主反射镜为抛物面镜，次反射镜的反射面为双曲面。

Concave reflecting surfaces of spherical cap, paraboloid and hyperboloid of revolution are investigated with regard to the dependence of the levitation force on the section radius Rb and curvature radius R of the reflector.

针对球面、旋转抛物面和旋转双曲面三种形状的凹面反射端，系统研究了悬浮力与反射端截面半径R_b和曲率半径R之间的本征关系。

Among the three concave reflecting surfaces, namely, a spherical cap, a paraboloid and a hyperboloid of revolution, the enhancement degree of FM for a spherical reflector is the largest.

在球面、旋转抛物面和旋转双曲面三种类型的凹面反射端中，采用球面反射端通过上述方式提高悬浮力，可以获得最佳效果。

In the paper, on the basis of aggregation of previous studies, the development of optical technology and development trends at home and abroad are introduced, the principle of Fresnel lens is summarized. In accordance with its principle, circle equidistant steps Fresnel lens design is described. And on this basis, based on Fresnel design, also based on a continuous upward spiral of the plane curve concept, incidence surface and the backlight is set up to greet Archimedes - Fresnel lens design formula and the Second parabolic type Fresnel lens design formula, and on this basis, the advantages and disadvantages of the three designs is discussed.

本文在充分了解非球面光学技术在国内外的发展状况和趋势的基础上，同时从菲涅尔透镜的光学原理出发，并根据它的工作原理推导了圆环等距菲涅尔透镜的设计步骤，并在此基础上依据菲涅尔的设计思想，同时依据平面曲线的连续又呈螺旋的构思，推导出了迎光面和背光面阿基米德型菲涅尔透镜的设计公式和二次抛物面型菲涅尔透镜的设计公式，并在此基础上讨论了这三种设计各自的优缺点。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。