catenoid

简明释义

英[ˈkætəˌnɔɪd]美[ˈkætəˌnɔɪd]

n. 悬线垂度；[数] 悬链曲面；悬索曲面

adj. 链状的

英英释义

单词用法

同义词

反义词

例句

1.During form-finding of catenoid, when the viscosity coefficient was not more than0.7, the dynamic relaxation method taking damp into account had good convergence and the nodes distributed more even.

对悬链面找形时发现，当黏性系数不大于0.7时，动力松弛法收敛，网格节点分布较无阻尼时均匀。

2.During form-finding of catenoid, when the viscosity coefficient was not more than0.7, the dynamic relaxation method taking damp into account had good convergence and the nodes distributed more even.

对悬链面找形时发现，当黏性系数不大于0.7时，动力松弛法收敛，网格节点分布较无阻尼时均匀。

3.Utility value is the matter agent of environmental economics value, utility value relation assumes catenoid or netlike structure.

效用价值是环境经济价值的物质承担者，效用价值关系呈链状或网状结构。

4.The soap film formed between two rings takes the shape of a catenoid when it is stable.

两个环之间形成的肥皂膜在稳定时呈现出悬链面的形状。

5.The design of the suspension bridge incorporates a catenoid shape to distribute weight evenly.

悬索桥的设计采用了悬链面形状，以均匀分配重量。

6.In architecture, a catenoid can be used to create aesthetically pleasing structures that are also strong.

在建筑中，悬链面可以用来创造既美观又坚固的结构。

7.Mathematicians study the properties of a catenoid to understand minimal surfaces.

数学家研究悬链面的性质，以理解最小表面。

8.A catenoid can be seen in the design of certain modern sculptures that emphasize curved lines.

在某些强调曲线的现代雕塑设计中，可以看到悬链面的身影。

作文

In the realm of mathematics and physics, the concept of a catenoid is quite fascinating. A catenoid is a type of minimal surface that can be formed by rotating a catenary curve around an axis. This unique shape has many practical applications in various fields, including architecture, engineering, and even biology. Understanding the properties of a catenoid can provide insights into the natural world and inspire innovative designs in human-made structures.To visualize a catenoid, imagine a soap film stretched between two circular rings. The surface formed by the soap film is a perfect example of a catenoid. It minimizes the surface area for a given boundary, which is a property that makes it particularly interesting to mathematicians. The mathematical equation that describes a catenoid involves hyperbolic functions, specifically the hyperbolic cosine. This connection to hyperbolic geometry is what gives the catenoid its distinct shape and properties.One of the remarkable features of a catenoid is its ability to maintain structural integrity while minimizing material usage. This characteristic is why architects often look to nature for inspiration. By studying the catenoid and other minimal surfaces, architects can create buildings that are not only aesthetically pleasing but also structurally sound. For instance, the design of certain bridges and roofs incorporates the principles of a catenoid to ensure stability while using less material than traditional designs.In addition to its architectural applications, the catenoid also appears in biological systems. Many organisms, such as certain types of shells and membranes, exhibit shapes that resemble a catenoid. This similarity suggests that the catenoid may play a role in the efficiency and functionality of these biological structures. Researchers study these natural forms to understand how they evolved and how they can inform new technologies.The study of catenoids also extends to the field of physics, particularly in understanding the behavior of liquids and gases. When analyzing the surface tension of a liquid, the shape of a catenoid can help explain how droplets form and how they interact with surfaces. This knowledge is crucial for various applications, from designing better containers to improving spray technologies.In conclusion, the catenoid is more than just a mathematical curiosity; it is a shape that embodies efficiency and beauty in both nature and human design. By exploring the properties and applications of the catenoid, we can gain a deeper appreciation for the interplay between mathematics, science, and art. Whether in the form of a stunning architectural masterpiece or a delicate biological structure, the catenoid serves as a reminder of the elegance found in the simplest of shapes.

在数学和物理的领域中，catenoid的概念非常迷人。catenoid是一种最小表面，可以通过围绕一个轴旋转一个悬链线曲线而形成。这种独特的形状在建筑、工程甚至生物学等多个领域都有许多实际应用。理解catenoid的性质可以为我们提供对自然世界的洞察，并激发人类设计中的创新。要想象catenoid，可以想象一层肥皂膜被拉伸在两个圆环之间。由肥皂膜形成的表面是catenoid的完美例子。它为给定边界最小化了表面积，这一特性使其对数学家特别有趣。描述catenoid的数学方程涉及双曲函数，特别是双曲余弦。这种与双曲几何的联系赋予了catenoid其独特的形状和性质。catenoid的一个显著特征是它在最小化材料使用的同时保持结构完整性。这一特性正是建筑师常常从自然中寻找灵感的原因。通过研究catenoid和其他最小表面，建筑师可以创造出不仅美观而且结构稳固的建筑。例如，某些桥梁和屋顶的设计结合了catenoid的原理，以确保稳定性，同时使用比传统设计更少的材料。除了建筑应用，catenoid还出现在生物系统中。许多生物体，如某些类型的贝壳和膜，展示出类似catenoid的形状。这种相似性表明，catenoid可能在这些生物结构的效率和功能中发挥作用。研究人员研究这些自然形态，以了解它们是如何进化的，以及它们如何能为新技术提供启示。对catenoid的研究也扩展到物理学领域，特别是在理解液体和气体的行为时。在分析液体的表面张力时，catenoid的形状可以帮助解释液滴是如何形成的以及它们如何与表面相互作用。这些知识对各种应用至关重要，从设计更好的容器到改善喷雾技术。总之，catenoid不仅仅是一个数学好奇心；它是一种在自然和人类设计中体现效率和美的形状。通过探索catenoid的性质和应用，我们可以更深入地欣赏数学、科学和艺术之间的相互作用。无论是作为令人惊叹的建筑杰作还是精致的生物结构，catenoid都提醒我们在最简单的形状中发现优雅。