paraboloid of revolution

简明释义

回转抛物面

英英释义

例句

1.The architectural feature of the building includes a large paraboloid of revolution dome that enhances acoustics.

这座建筑的建筑特色包括一个大型的旋转抛物面穹顶，增强了声学效果。

2.The design of this modern lamp resembles a paraboloid of revolution, providing uniform light distribution.

这款现代灯具的设计类似于旋转抛物面，提供均匀的光分布。

3.In physics, the trajectory of a projectile can be modeled as a paraboloid of revolution under certain conditions.

在物理学中，某些条件下，投射物的轨迹可以建模为旋转抛物面。

4.Engineers often use a paraboloid of revolution shape for reflectors to enhance the efficiency of solar panels.

工程师们常常使用旋转抛物面形状的反射器来提高太阳能电池板的效率。

5.The satellite dish is designed in the shape of a paraboloid of revolution to focus signals effectively.

卫星天线的设计呈现为旋转抛物面的形状，以有效聚焦信号。

作文

In the realm of geometry and engineering, the term paraboloid of revolution refers to a three-dimensional surface that is generated by rotating a parabola around its axis of symmetry. This fascinating shape has numerous applications in various fields, including architecture, optics, and satellite dish design. Understanding the properties and significance of the paraboloid of revolution can provide insights into both theoretical concepts and practical implementations.To visualize a paraboloid of revolution, imagine a standard parabola, which is typically defined by the equation y = ax². When this curve is rotated around the vertical axis (the axis of symmetry), it creates a surface that resembles a bowl or a satellite dish. The mathematical representation of a paraboloid of revolution can be expressed in Cartesian coordinates as z = ax² + by², where 'a' and 'b' are constants that determine the curvature of the surface.One of the most notable features of the paraboloid of revolution is its reflective property. This characteristic makes it particularly useful in the design of parabolic mirrors and antennas. For instance, in a parabolic mirror, parallel rays of light that enter the mirror will reflect off the surface and converge at a single focal point. This principle is utilized in telescopes and solar concentrators, where focusing light is essential for their functionality.In architecture, the aesthetic appeal and structural integrity of the paraboloid of revolution have led to its incorporation in modern designs. Buildings with curved surfaces not only stand out visually but also distribute weight more efficiently. The Sydney Opera House, for example, features shells that can be approximated by paraboloids of revolution, showcasing how mathematics can influence art and engineering.Moreover, the paraboloid of revolution finds its place in the field of physics, particularly in the study of gravitational fields. The shape is relevant when analyzing the potential energy of objects in a gravitational field, where the surface can represent the locus of points at a constant potential energy level. This connection between geometry and physical principles highlights the interdisciplinary nature of studying shapes like the paraboloid of revolution.In conclusion, the paraboloid of revolution is more than just a geometric figure; it is a fundamental shape that bridges various disciplines, including mathematics, physics, engineering, and art. Its unique properties and applications make it an essential concept to understand for anyone interested in the interplay between form and function. By exploring the characteristics and uses of the paraboloid of revolution, we gain a deeper appreciation for the beauty and complexity of the world around us, revealing how mathematical concepts manifest in tangible ways. As we continue to innovate and design, the paraboloid of revolution will undoubtedly remain a pivotal element in both theoretical explorations and practical applications.

在几何和工程领域，术语旋转抛物面指的是一种三维表面，它是通过围绕其对称轴旋转抛物线而生成的。这种迷人的形状在建筑、光学和卫星天线设计等多个领域中有着广泛的应用。理解旋转抛物面的特性和意义可以为理论概念和实际应用提供见解。要想象旋转抛物面，可以想象一个标准的抛物线，通常由方程y = ax²定义。当这个曲线围绕垂直轴（对称轴）旋转时，会形成一个类似碗或卫星天线的表面。旋转抛物面的数学表示可以用笛卡尔坐标系表示为z = ax² + by²，其中'a'和'b'是决定表面曲率的常数。旋转抛物面最显著的特点之一是其反射特性。这一特性使其在抛物面镜和天线设计中尤为有用。例如，在抛物面镜中，平行的光线进入镜子后将反射到表面并汇聚在一个焦点上。这一原理被用于望远镜和太阳能集中器中，聚焦光线对于它们的功能至关重要。在建筑学中，旋转抛物面的美学吸引力和结构完整性使其被纳入现代设计中。具有曲面形状的建筑不仅在视觉上引人注目，而且能更有效地分配重量。例如，悉尼歌剧院的外壳可以近似为旋转抛物面，展示了数学如何影响艺术和工程。此外，旋转抛物面在物理学领域也有其位置，特别是在研究重力场时。当分析物体在重力场中的势能时，这种形状是相关的，其中该表面可以表示在某个恒定势能水平上的点的轨迹。几何与物理原理之间的这种联系突显了研究像旋转抛物面这样的形状的跨学科性质。总之，旋转抛物面不仅仅是一个几何图形；它是一种基础形状，连接了数学、物理、工程和艺术等多个学科。它独特的特性和应用使其成为任何对形式与功能之间的相互作用感兴趣的人必须理解的概念。通过探索旋转抛物面的特征和用途，我们对周围世界的美丽和复杂性有了更深的理解，揭示了数学概念如何以具体的方式表现出来。随着我们继续创新和设计，旋转抛物面无疑将继续作为理论探索和实际应用中的关键元素。