tractrix

简明释义

英[ˈtræktrɪks]美[ˈtræktrɪks]

n. [数] 曳物线；等切距曲线

复 数 t r a c t r i c e s

英英释义

单词用法

同义词

反义词

例句

1.In the "Acta" of 1691 James Bernoulli derived the equation for the tractrix.

在1691年的《学报》中詹姆士·伯努利推导出跟踪曲线的方程。

2.In the "Acta" of 1691 James Bernoulli derived the equation for the tractrix.

在1691年的《学报》中詹姆士·伯努利推导出跟踪曲线的方程。

3.The path of the falling object can be modeled using a tractrix.

下落物体的轨迹可以用tractrix来建模。

4.The tractrix is essential in understanding how objects move through fluid mediums.

tractrix对于理解物体如何在流体介质中移动至关重要。

5.In physics, a tractrix is often used to describe the motion of an object under gravity.

在物理学中，tractrix常用于描述物体在重力作用下的运动。

6.Engineers use a tractrix curve to optimize the trajectory of projectiles.

工程师使用tractrix曲线来优化弹丸的轨迹。

7.The design of the water slide incorporates a tractrix shape for better flow.

水滑梯的设计采用了tractrix形状，以实现更好的水流。

作文

In the realm of mathematics and physics, the concept of a curve plays a significant role in understanding various phenomena. One such intriguing curve is known as the tractrix, which has unique properties that make it particularly interesting for both theoretical exploration and practical applications. The term tractrix refers to a specific type of curve that is defined as the path traced by an object being pulled along a straight line at a constant speed. This curve has fascinating characteristics that distinguish it from other curves in mathematics.The tractrix can be visualized as the trajectory of a particle that is constrained to move towards a fixed point while being pulled by a force. Imagine a scenario where a person is walking a dog on a leash; as the dog moves away from the person, the leash creates a tractrix shape in the air. This analogy helps to illustrate how the tractrix represents the relationship between the pulling force and the path taken by the object.Mathematically, the tractrix can be described using parametric equations or polar coordinates, depending on the context. Its equation reveals that as the distance from the fixed point increases, the slope of the tractrix decreases, leading to an asymptotic behavior towards the horizontal axis. This unique property makes the tractrix highly relevant in various fields, including engineering, physics, and even biology.One of the most notable applications of the tractrix is in the design of certain types of curves in mechanical systems, such as gears and pulleys. Engineers often utilize the properties of the tractrix to create efficient systems that minimize friction and maximize performance. For instance, when designing a roller coaster, engineers must consider the forces acting on the riders, and the tractrix can provide insights into how to shape the track for optimal safety and enjoyment.Moreover, the tractrix also finds its place in the study of fluid dynamics, particularly in analyzing the flow of fluids around objects. Understanding the tractrix allows scientists to predict how fluids will behave when encountering obstacles, which is crucial for designing efficient transportation systems, such as airplanes and ships. By studying the tractrix, researchers can develop models that enhance our understanding of airflow and water currents, ultimately leading to innovations in various industries.In addition to its practical implications, the tractrix also holds aesthetic value in art and design. Artists and architects may draw inspiration from the elegant curves of the tractrix to create visually appealing structures and compositions. The smooth and continuous nature of the tractrix can evoke feelings of grace and fluidity, making it a popular choice for creative endeavors.In conclusion, the tractrix is more than just a mathematical concept; it is a versatile curve with applications spanning multiple disciplines. From engineering to art, the tractrix exemplifies the interconnectedness of mathematics and the real world. By exploring the properties and implications of the tractrix, we gain valuable insights into both the abstract realm of mathematics and the tangible challenges faced in various fields. Understanding the tractrix not only enriches our knowledge of curves but also enhances our ability to innovate and create in a world that is constantly evolving.

在数学和物理的领域中，曲线的概念在理解各种现象方面发挥着重要作用。其中一个引人入胜的曲线被称为tractrix，它具有独特的性质，使其在理论探索和实际应用中都特别有趣。术语tractrix指的是一种特定类型的曲线，它被定义为在恒定速度下沿直线被拉动的物体所描绘的路径。这条曲线具有迷人的特征，使其与数学中的其他曲线区分开来。可以将tractrix视为一个粒子的轨迹，该粒子被限制在向固定点移动的同时受到一个力的拉动。想象一个场景，一个人正在牵狗散步；当狗远离这个人时，牵引绳在空中形成了tractrix形状。这个比喻有助于说明tractrix如何代表拉动力与物体所走路径之间的关系。从数学上讲，tractrix可以通过参数方程或极坐标来描述，具体取决于上下文。它的方程揭示了随着距离固定点的增加，tractrix的斜率减小，导致向水平轴的渐近行为。这一独特属性使得tractrix在工程、物理甚至生物学等多个领域中高度相关。tractrix最显著的应用之一是在某些机械系统中曲线的设计，例如齿轮和滑轮。工程师们经常利用tractrix的特性来创建高效的系统，以最小化摩擦并最大化性能。例如，在设计过山车时，工程师必须考虑作用于乘客的力量，而tractrix可以提供有关如何塑造轨道以实现最佳安全性和乐趣的见解。此外，tractrix还在流体动力学研究中占有一席之地，特别是在分析流体绕物体流动时。理解tractrix使科学家能够预测流体在遇到障碍物时的行为，这对设计高效的运输系统（如飞机和船只）至关重要。通过研究tractrix，研究人员可以开发模型，增强我们对气流和水流的理解，最终推动各个行业的创新。除了其实际意义外，tractrix在艺术和设计中也具有美学价值。艺术家和建筑师可能会从tractrix优雅的曲线中获得灵感，以创造视觉上吸引人的结构和作品。tractrix的平滑和连续特性可以唤起优雅和流畅的感觉，使其成为创意工作的热门选择。总之，tractrix不仅仅是一个数学概念；它是一条多学科应用的多功能曲线。从工程到艺术，tractrix体现了数学与现实世界的相互联系。通过探索tractrix的性质和影响，我们获得了关于数学抽象领域和各个领域面临的切实挑战的宝贵见解。理解tractrix不仅丰富了我们对曲线的知识，还增强了我们在不断发展的世界中创新和创造的能力。