evolute

简明释义

英[ˈevəluːt]美[ˈevəˌlʊt]

n. 渐屈线，发包线

adj. 展开的，反卷的

复 数 e v o l u t e s

英英释义

单词用法

同义词

反义词

例句

1.When the point moves along the plane curve , the trace curve of the point is called the evolute of the curve , denoted by, and is called the involute of the curve .

当点沿曲线移动时，相应的曲率中心的轨迹曲线称为曲线的渐屈线，而曲线称为曲线的渐伸线。

2.When the point moves along the plane curve , the trace curve of the point is called the evolute of the curve , denoted by, and is called the involute of the curve .

当点沿曲线移动时，相应的曲率中心的轨迹曲线称为曲线的渐屈线，而曲线称为曲线的渐伸线。

3.Rudders used in China's vessels did evolute from oars according to the undoubted excavated cultural relics and the relics handed down from ancient times.

据确凿无疑的出土的及传世的文物，中国船舶的舵是由桨演变而来的。

4.However, the cyber media has been keeping a close contact with the traditional media, that is, they coexist and co-evolute.

但是，网络媒体与传统媒体却又保持着密切地联系，即共同相处、共同演进。

5.The giants in this generation is very possibly becoming the shortsin the next generation, since the times evolute.

这一时代的巨人很有可能是下一时代的矮子，因为时代在变。

6.Process of parametric modeling of bevel gear with standard evolute tooth on PC based CAD system is presented.

提出实体参数化逆向造型设计的方法，介绍应用该方法开发圆锥齿轮三维实体参数化造型设计系统的过程。

7.Technological innovation is a complicated system, and this system always evolute from inferior to upper.

技术创新是一个复杂的系统，而这个系统总是从低级向高级进化的。

8.He then treated the evolute of a plane curve.

然后他讨论了平面曲线的渐屈线。

9.The curve's evolute represents the path traced by the center of curvature.

曲线的evolute表示由曲率中心描绘的路径。

10.In geometry, understanding the evolute can help visualize the properties of curves.

在几何学中，理解evolute可以帮助可视化曲线的性质。

11.The evolute of a circle is a single point at its center.

圆的evolute是其中心的一个点。

12.Mathematicians study the evolute to gain insights into the behavior of complex shapes.

数学家研究evolute以深入了解复杂形状的行为。

13.The evolute can be used in engineering to design smoother transitions between parts.

在工程中，evolute可以用于设计零件之间更平滑的过渡。

作文

In the realm of mathematics, the concept of an evolute is a fascinating topic that merges geometry and calculus. An evolute is essentially the locus of all the centers of curvature of a given curve. This means that if you take any point on a curve and draw a circle that best approximates the curve at that point, the center of that circle will lie on the evolute of the original curve. Understanding this concept not only deepens our appreciation for the beauty of curves but also enhances our ability to analyze their properties. To illustrate this further, let's consider a simple example: a circle. The evolute of a circle is a single point, which is the center of the circle itself. This is because every point on the circle has the same radius of curvature, leading to a constant center. However, when we examine more complex shapes, such as an ellipse or a parabola, the evolute becomes much more intricate. For instance, the evolute of an ellipse consists of two separate branches, each representing the curvature of the ellipse at different points. The significance of the evolute extends beyond pure mathematics; it finds applications in various fields such as physics, engineering, and computer graphics. In physics, understanding the evolute can help in studying motion along curved paths, while in engineering, it assists in designing components that must fit together smoothly. Furthermore, in computer graphics, the evolute can be utilized to create realistic animations of objects moving along curved trajectories. Moreover, the relationship between a curve and its evolute highlights the importance of curvature in understanding the shape and behavior of curves. Curvature is a measure of how quickly a curve changes direction, and by analyzing the evolute, we can gain insights into the nature of the original curve. For example, if a curve has regions of high curvature, the evolute will reflect this by having sharp turns and bends. Conversely, a curve with low curvature will yield a smoother evolute. In conclusion, the study of the evolute enriches our comprehension of curves and their properties. It serves as a bridge between geometry and calculus, providing a deeper understanding of how curves behave and interact with their surroundings. As we continue to explore the intricacies of mathematics, the evolute stands out as a remarkable concept that showcases the elegance and complexity of geometric relationships. By embracing the knowledge of the evolute, we can enhance our analytical skills and apply these principles to real-world problems, ultimately appreciating the profound connections that mathematics has with the world around us.

在数学领域，evolute的概念是一个迷人的话题，它将几何与微积分结合在一起。evolute本质上是给定曲线所有曲率中心的轨迹。这意味着，如果你取曲线上的任何一点，并画出一个在该点最佳近似曲线的圆，那么这个圆的中心将位于原始曲线的evolute上。理解这个概念不仅加深了我们对曲线美的欣赏，还增强了我们分析其属性的能力。 为了进一步说明这一点，让我们考虑一个简单的例子：一个圆。圆的evolute是一个单一的点，即圆的中心。这是因为圆上的每个点都有相同的曲率半径，导致中心恒定。然而，当我们研究更复杂的形状，如椭圆或抛物线时，evolute变得更加复杂。例如，椭圆的evolute由两个独立的分支组成，每个分支代表椭圆在不同点的曲率。 evolute的重要性超越了纯数学，它在物理学、工程学和计算机图形学等多个领域都有应用。在物理学中，理解evolute可以帮助研究沿曲线路径的运动，而在工程学中，它有助于设计必须平滑结合的组件。此外，在计算机图形学中，evolute可用于创建沿曲线路径移动的物体的真实动画。 此外，曲线与其evolute之间的关系突显了曲率在理解曲线形状和行为中的重要性。曲率是衡量曲线变化方向快慢的指标，通过分析evolute，我们可以深入了解原始曲线的性质。例如，如果一条曲线具有高曲率区域，那么evolute将通过急转弯和弯曲来反映这一点。相反，低曲率的曲线将产生更平滑的evolute。 总之，evolute的研究丰富了我们对曲线及其属性的理解。它作为几何与微积分之间的桥梁，提供了对曲线如何表现和与周围环境互动的更深刻理解。随着我们继续探索数学的复杂性，evolute作为一个杰出的概念，展示了几何关系的优雅与复杂性。通过接受evolute的知识，我们可以增强我们的分析技能，并将这些原理应用于现实世界的问题，从而最终欣赏数学与我们周围世界之间深刻的联系。