surface of revolution

简明释义

旋转面

英英释义

例句

1.The design of the vase is based on a surface of revolution (旋转曲面) that creates a beautiful shape.

这个花瓶的设计是基于一个surface of revolution (旋转曲面)，形成了美丽的形状。

2.The surface of revolution (旋转曲面) can be used to model various objects in engineering.

在工程中，可以使用surface of revolution (旋转曲面) 来建模各种物体。

3.Artists often use the concept of surface of revolution (旋转曲面) to create sculptures with symmetry.

艺术家们常常利用surface of revolution (旋转曲面) 的概念来创作对称的雕塑。

4.A classic example of a surface of revolution (旋转曲面) is a sphere, created by rotating a circle.

一个经典的surface of revolution (旋转曲面) 示例是球体，它是通过旋转一个圆圈形成的。

5.In calculus, we often calculate the volume of solids formed by rotating a surface of revolution (旋转曲面) around an axis.

在微积分中，我们常常计算通过围绕轴旋转的surface of revolution (旋转曲面) 形成的固体体积。

作文

In the field of mathematics and geometry, the concept of a surface of revolution is fundamental in understanding how shapes can be generated through rotation. A surface of revolution is defined as a surface created by rotating a two-dimensional curve around a straight line that lies in the same plane as the curve. This process allows for the creation of various three-dimensional objects, each with unique properties and applications.For instance, consider the simple case of rotating a circle around its diameter. The resulting surface of revolution is a sphere, a shape that is perfectly symmetrical and has many practical applications in both science and engineering. Similarly, if we take a rectangle and rotate it about one of its edges, we create a cylinder, another common surface of revolution. These examples illustrate how different two-dimensional shapes can yield diverse three-dimensional forms when subjected to rotational motion.The significance of surface of revolution extends beyond mere geometry; it plays a critical role in various fields such as physics, engineering, and computer graphics. In physics, for example, the understanding of surface of revolution is essential when analyzing objects in motion or studying the properties of materials. Engineers often utilize these surfaces in designing components that must withstand specific stresses and strains, ensuring that they are both functional and efficient.Moreover, in computer graphics, the creation of realistic three-dimensional models often relies on the principles of surface of revolution. By defining a shape in two dimensions and rotating it, graphic designers can produce intricate models that mimic real-world objects. This technique is widely used in animation, video game design, and virtual reality, allowing creators to bring their visions to life with impressive detail and accuracy.To further understand the mathematical implications of surface of revolution, one can explore the equations that define these surfaces. For example, the equation for a sphere of radius r centered at the origin is given by x² + y² + z² = r². When this sphere is derived from rotating a semicircle around the x-axis, it becomes clear how the surface of revolution is not just a theoretical concept but a tangible mathematical construct.In conclusion, the surface of revolution is an essential concept in mathematics and its applications. By rotating two-dimensional shapes, we can create a variety of three-dimensional forms that have significant implications in numerous fields. Understanding this concept enriches our comprehension of geometry and enhances our ability to apply mathematical principles to solve real-world problems. Whether in engineering, physics, or computer graphics, the surface of revolution remains a powerful tool for innovation and creativity.

在数学和几何学领域，旋转曲面的概念对于理解形状如何通过旋转生成是基础性的。旋转曲面被定义为通过将一个二维曲线围绕一条位于同一平面内的直线旋转而形成的表面。这个过程允许生成各种三维物体，每个物体都有独特的属性和应用。例如，考虑将一个圆绕其直径旋转的简单情况。结果的旋转曲面是一个球体，这是一种完美对称的形状，在科学和工程中有许多实际应用。类似地，如果我们取一个矩形并绕其一个边旋转，我们就会创建一个圆柱体，这是另一个常见的旋转曲面。这些例子说明了不同的二维形状在经历旋转运动时如何产生多样的三维形式。旋转曲面的重要性超越了单纯的几何学；它在物理学、工程学和计算机图形学等多个领域中起着关键作用。例如，在物理学中，理解旋转曲面对于分析运动中的物体或研究材料的性质至关重要。工程师通常利用这些表面设计必须承受特定应力和应变的组件，确保它们既功能性又高效。此外，在计算机图形学中，创建逼真的三维模型往往依赖于旋转曲面的原理。通过在二维中定义一个形状并进行旋转，图形设计师可以生成复杂的模型，模拟现实世界的物体。这种技术广泛应用于动画、视频游戏设计和虚拟现实，使创作者能够以令人印象深刻的细节和准确性将他们的愿景变为现实。为了进一步理解旋转曲面的数学意义，可以探索定义这些表面的方程。例如，半径为r的以原点为中心的球体的方程为x² + y² + z² = r²。当这个球体是由围绕x轴旋转的半圆得出的时，显然旋转曲面不仅仅是一个理论概念，而是一个具体的数学构造。总之，旋转曲面是数学及其应用中的一个基本概念。通过旋转二维形状，我们可以创造出多种具有重要意义的三维形式。在工程、物理或计算机图形学中，理解这一概念丰富了我们对几何学的理解，并增强了我们应用数学原理解决现实问题的能力。无论是在工程、物理还是计算机图形学中，旋转曲面始终是创新和创造力的强大工具。