hyperboloid of revolution

简明释义

回转双曲面

英英释义

例句

1.In physics, the hyperboloid of revolution can model certain types of gravitational fields.

在物理学中，旋转双曲面可以模拟某些类型的引力场。

2.The mathematician explained how to derive the equation of a hyperboloid of revolution using conic sections.

数学家解释了如何通过圆锥曲线推导出旋转双曲面的方程。

3.The artist chose a hyperboloid of revolution as the theme for her sculpture, emphasizing its elegant curves.

艺术家选择旋转双曲面作为她雕塑的主题，强调其优雅的曲线。

4.The cooling tower design features a distinctive shape known as a hyperboloid of revolution, which enhances airflow efficiency.

冷却塔的设计采用了一个独特的形状，称为旋转双曲面，这提高了空气流动效率。

5.In architecture, the hyperboloid of revolution is often used for creating visually striking structures.

在建筑中，旋转双曲面常用于创造视觉上引人注目的结构。

作文

The concept of a hyperboloid of revolution is an intriguing topic in the field of geometry and engineering. A hyperboloid of revolution is a three-dimensional surface generated by rotating a hyperbola around one of its principal axes. This fascinating shape exhibits unique properties that make it applicable in various real-world scenarios, particularly in architecture and structural design. To understand the hyperboloid of revolution, we must first consider the characteristics of a hyperbola. A hyperbola consists of two separate curves that open away from each other, and when one of these curves is rotated around an axis, it forms a surface that is both aesthetically pleasing and structurally sound. The resulting hyperboloid of revolution can take on different forms depending on the orientation and dimensions of the hyperbola being rotated. One of the most notable examples of a hyperboloid of revolution in architecture is the cooling towers of power plants. These structures are designed in the shape of a hyperboloid to optimize airflow and cooling efficiency. The design not only serves a functional purpose but also provides a visually striking silhouette against the skyline. The hyperboloid shape allows for a wide base that tapers as it rises, creating a stable structure capable of withstanding strong winds and other environmental forces. In addition to its architectural applications, the hyperboloid of revolution has significant implications in the field of mathematics and physics. It is often used to model phenomena such as gravitational fields and light propagation. The mathematical equations governing the hyperboloid of revolution can be complex, involving hyperbolic functions and conic sections, but they provide valuable insights into the behavior of various physical systems. Moreover, the hyperboloid of revolution is also relevant in the realm of computer graphics and design. In 3D modeling software, this geometric shape can be easily created and manipulated, allowing designers to explore its aesthetic qualities and structural integrity. The ability to generate a hyperboloid of revolution digitally opens up new avenues for creativity in art and design, enabling artists to push the boundaries of traditional forms. In conclusion, the hyperboloid of revolution is more than just a mathematical abstraction; it represents a convergence of art, science, and engineering. Its unique properties and applications make it a fascinating subject of study, inspiring innovations in various fields. As we continue to explore the complexities of shapes and structures, the hyperboloid of revolution stands out as a remarkable example of how geometry can influence our world. Understanding this shape not only enhances our comprehension of mathematical concepts but also enriches our appreciation for the beauty found in the intersection of mathematics and the physical world.

旋转双曲面是几何和工程领域中的一个引人入胜的主题。旋转双曲面是通过围绕其主轴旋转双曲线而生成的三维表面。这种迷人的形状展示了独特的属性，使其在建筑和结构设计等各种现实世界场景中具有应用价值。要理解旋转双曲面，我们首先必须考虑双曲线的特征。双曲线由两个分开的曲线组成，它们相互远离，当其中一条曲线围绕一个轴旋转时，就形成了一种既美观又结构稳固的表面。生成的旋转双曲面可以根据被旋转的双曲线的方向和尺寸呈现不同的形式。旋转双曲面的一个显著例子是在电厂的冷却塔。这些结构呈现出双曲面的形状，以优化气流和冷却效率。这种设计不仅服务于功能目的，还为天际线提供了视觉上引人注目的轮廓。双曲面形状允许宽大的基础向上收缩，形成一种稳定的结构，能够承受强风和其他环境力量。除了建筑应用外，旋转双曲面在数学和物理学领域也具有重要意义。它常用于建模诸如重力场和光传播等现象。控制旋转双曲面的数学方程可能很复杂，涉及双曲函数和圆锥曲线，但它们为各种物理系统的行为提供了有价值的见解。此外，旋转双曲面在计算机图形和设计领域也相关。在3D建模软件中，可以轻松创建和操纵这种几何形状，使设计师能够探索其美学特质和结构完整性。数字生成旋转双曲面的能力为艺术和设计中的创造力开辟了新途径，使艺术家能够突破传统形式的界限。总之，旋转双曲面不仅仅是一个数学抽象；它代表了艺术、科学和工程的交汇。它独特的属性和应用使其成为值得研究的迷人主题，激发了各个领域的创新。当我们继续探索形状和结构的复杂性时，旋转双曲面作为几何学如何影响我们世界的一个杰出例子脱颖而出。理解这一形状不仅增强了我们对数学概念的理解，还丰富了我们对数学与物理世界交集中的美的欣赏。