hyperboloid

简明释义

英[haɪˈpɜːbəˌlɔɪd]美[haɪˈpɜːrbəˌlɔɪd]

n. [数] 双曲面；双曲线体

英英释义

单词用法

同义词

反义词

例句

1.Transition to the three-dimensional space, then we obtain the equation of equipotential surface families of charged conductor with surface of hyperboloid of one sheet.

利用保角变换，首先在二维平面得到双曲线型的等位线簇方程，然后过渡到三维空间，从而得到表面为单叶双曲面（两实半轴相等）的带电导体的等位面簇方程。

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

单叶双曲面和双曲抛物面是直线曲面。

3.In this paper, the dynamic problems of hyperboloid latticed flat shells are studied by using the method of simulated shell.

本文利用拟壳法研究了双曲率网状扁壳的动力问题。

4.Mathematical model for hyperboloid grinding of twist drill and relationships between drill design and grinding parameters are introduced.

基于非共轴螺旋面钻尖的刃磨原理，建立了刃磨参数的数学模型。

5.Two of them intersect in a curved line which in turn intersects with the third hyperboloid in a point corresponding to the unknown three-dimensional user position.

两个曲面相交得到一条曲线，曲线与第三个曲面的交点既是用户的三维坐标。

6.Mathematical model for hyperboloid grinding of twist drill and relationships between drill design and grinding parameters are introduced.

介绍了以回转双曲面作为麻花钻后刀面的数学模型，设计参数与刃磨参数的关系。

7.The ceiling system should satisfy these requirements that using lower chord ball as fixed point, adapting space change of hyperboloid steel grid, grid settlement under snow load.

其天花体系要满足以屋面网架下弦球为固定点和适应双曲面的空间变化、网架雪荷载作用下沉、热胀冷缩等变形运动。

8.In mathematics, a hyperboloid can be defined as a surface generated by rotating a hyperbola around one of its principal axes.

在数学中，双曲面可以定义为通过围绕其一个主轴旋转双曲线生成的表面。

9.The cooling tower of the power plant is shaped like a hyperboloid to enhance airflow and efficiency.

发电厂的冷却塔呈双曲面形状，以增强气流和效率。

10.The hyperboloid shape is commonly found in modern sculptures and installations due to its aesthetic appeal.

由于其美学吸引力，双曲面形状通常出现在现代雕塑和装置艺术中。

11.Engineers often use hyperboloid designs in structures to ensure stability and strength.

工程师们经常在结构中使用双曲面设计，以确保稳定性和强度。

12.The architect designed a stunning building with a hyperboloid structure that captures the light beautifully.

建筑师设计了一座令人惊叹的建筑，采用了双曲面结构，能够美妙地捕捉光线。

作文

The world of geometry is filled with fascinating shapes and structures, each with its own unique properties and applications. One such shape that stands out in the realm of three-dimensional geometry is the hyperboloid. A hyperboloid is a type of surface that can be classified into two main categories: the hyperboloid of one sheet and the hyperboloid of two sheets. These surfaces are generated by rotating a hyperbola around its axis, resulting in a strikingly beautiful and intricate form.The hyperboloid of one sheet resembles a cooling tower or a vase, tapering at the top and bottom while bulging in the middle. This shape is not only aesthetically pleasing but also structurally significant. It is commonly used in architecture and engineering due to its ability to distribute stress evenly across its surface. For instance, the famous TWA Flight Center at New York's JFK Airport, designed by Eero Saarinen, features a stunning hyperboloid structure that captures the eye and embodies the spirit of modern design.On the other hand, the hyperboloid of two sheets appears as two separate, mirror-image surfaces that do not connect. This form is less common in practical applications but remains an important subject of study in mathematics and physics. The mathematical equations governing these surfaces reveal much about their properties and behavior, allowing scientists and engineers to model various physical phenomena.In addition to their architectural significance, hyperboloids also play a crucial role in various scientific fields. For example, in optics, hyperboloidal mirrors are used to focus light and create images. The unique curvature of a hyperboloid allows for precise manipulation of light rays, making it an essential component in telescopes and other optical devices. Furthermore, in the field of thermodynamics, the concept of a hyperboloid is used to describe certain types of energy states, illustrating the interconnectedness of geometry and physics.To further understand the significance of hyperboloids, one must delve into their mathematical properties. The equations that define a hyperboloid can be expressed in Cartesian coordinates, and they exhibit unique characteristics such as asymptotic behavior and curvature. These mathematical properties not only provide insight into the nature of hyperboloids but also allow mathematicians to explore related concepts, such as hyperbolic functions and surfaces.In conclusion, the hyperboloid is a remarkable geometric shape that transcends mere aesthetics. Its applications in architecture, optics, and physics demonstrate the profound connection between mathematics and the physical world. As we continue to explore the complexities of geometry, the hyperboloid remains a symbol of innovation and creativity, inspiring future generations of scientists, engineers, and artists alike. Understanding and mastering the concept of hyperboloid opens up new avenues for exploration and discovery, reminding us of the beauty inherent in the mathematical structures that surround us. Whether through its structural integrity in buildings or its functionality in scientific instruments, the hyperboloid serves as a testament to the power and elegance of geometry.

几何学的世界充满了迷人的形状和结构，每种形状都有其独特的属性和应用。其中在三维几何学领域中脱颖而出的一个形状是双曲面。双曲面是一种表面，可以分为两大类：单层双曲面和双层双曲面。这些表面是通过围绕其轴旋转双曲线生成的，形成了一种引人注目的美丽和复杂的形状。单层双曲面类似于冷却塔或花瓶，顶部和底部逐渐收窄，而中间则鼓起。这个形状不仅美观，而且在结构上具有重要意义。由于它能够均匀分配表面上的压力，因此通常用于建筑和工程中。例如，纽约JFK机场著名的TWA航班中心，由Eero Saarinen设计，具有令人惊叹的双曲面结构，吸引了眼球，并体现了现代设计的精神。另一方面，双层双曲面看起来像两个独立的、镜像的表面，它们不连接。这种形式在实际应用中较少见，但在数学和物理学的研究中仍然是一个重要的研究对象。描述这些表面的数学方程揭示了它们的许多特性和行为，使科学家和工程师能够对各种物理现象进行建模。除了在建筑中的重要性外，双曲面在多个科学领域也发挥着关键作用。例如，在光学中，双曲面镜用于聚焦光线并创建图像。双曲面的独特曲率允许精确操控光线，使其成为望远镜和其他光学设备中的重要组成部分。此外，在热力学领域，双曲面的概念用于描述某些类型的能量状态，说明了几何学与物理学之间的相互联系。为了进一步理解双曲面的重要性，人们必须深入研究其数学属性。定义双曲面的方程可以用笛卡尔坐标表示，并且它们表现出独特的特征，如渐近行为和曲率。这些数学属性不仅提供了对双曲面本质的洞察，还使数学家能够探索相关概念，如双曲函数和表面。总之，双曲面是一种非凡的几何形状，超越了单纯的美学。它在建筑、光学和物理学中的应用展示了数学与物理世界之间深刻的联系。当我们继续探索几何学的复杂性时，双曲面仍然是创新和创造力的象征，激励着未来一代科学家、工程师和艺术家。理解和掌握双曲面的概念为探索和发现开辟了新的途径，提醒我们周围数学结构中固有的美。无论是通过其在建筑中的结构完整性，还是在科学仪器中的功能性，双曲面都证明了几何学的力量和优雅。