excess of arc

简明释义

余弧

英英释义

例句

1.In the analysis, we found that the excess of arc in the path caused unnecessary friction.

在分析中，我们发现路径中的弧度过大导致了不必要的摩擦。

2.The engineer noted an excess of arc in the bridge's design, which could lead to structural issues.

工程师注意到桥梁设计中存在弧度过大，这可能导致结构问题。

3.During the simulation, we observed an excess of arc in the trajectory, affecting the overall performance.

在模拟过程中，我们观察到轨迹中有弧度过大，影响了整体性能。

4.The architect had to revise the plans due to an excess of arc in the roof structure.

由于屋顶结构中存在弧度过大，建筑师不得不修改计划。

5.The artist's painting had an excess of arc in the background, creating a sense of depth.

艺术家的画作背景中有弧度过大，营造出一种深度感。

作文

The concept of an excess of arc is often encountered in various fields of mathematics and physics, particularly in the study of circles and angles. To understand this term, we first need to delve into the fundamentals of circular geometry. In a circle, an arc is a segment of the circumference, defined by two endpoints. The excess of arc refers to the amount by which the length of an arc exceeds a certain reference length, typically the length of a corresponding central angle in radians. For example, if we consider a circle with a radius of one unit, the total circumference is 2π. If we take a central angle of 90 degrees, which is equivalent to π/2 radians, the length of the arc subtended by this angle is (π/2) * 1 = π/2. However, if we were to measure an arc that subtends a larger angle, say 120 degrees or 2π/3 radians, the length of this arc would be (2π/3) * 1 = 2π/3. The excess of arc in this case would be the difference between the lengths of these two arcs, which can be calculated as follows: 2π/3 - π/2 = (4π - 3π)/6 = π/6. This excess represents how much longer the 120-degree arc is compared to the 90-degree arc.Understanding the excess of arc is crucial in applications such as engineering and architecture, where precise measurements are essential. For instance, when designing curved structures, engineers must account for the excess of arc to ensure that the materials used can withstand the forces exerted on them. Additionally, in navigation and astronomy, the excess of arc becomes significant when calculating distances between points on the Earth's surface, especially when using spherical models. Moreover, the excess of arc can also be linked to concepts in calculus, particularly when dealing with integrals that calculate the length of curves. By understanding how to compute the excess of arc, students and professionals can apply this knowledge to real-world problems, enhancing their analytical skills and mathematical reasoning.In conclusion, the excess of arc is a fundamental concept in geometry that extends beyond theoretical mathematics into practical applications across various disciplines. By grasping this idea, individuals can develop a deeper appreciation for the intricacies of circular motion and the relationships between angles and arc lengths. As we continue to explore the fascinating world of geometry, the excess of arc will undoubtedly remain an important topic for further study and application.

“弧的超出”这一概念常常出现在数学和物理的多个领域，特别是在圆和角度的研究中。为了理解这个术语，我们首先需要深入了解圆形几何的基本原理。在一个圆中，弧是由两个端点定义的圆周的一段。弧的超出指的是弧的长度超过某个参考长度的量，通常是对应中央角（以弧度表示）的长度。例如，如果我们考虑一个半径为1单位的圆，整个周长是2π。如果我们取一个90度的中央角，它等于π/2弧度，那么这个角所涵盖的弧的长度为(π/2) * 1 = π/2。然而，如果我们测量一个涵盖更大角度的弧，比如120度或2π/3弧度，这个弧的长度将是(2π/3) * 1 = 2π/3。在这种情况下，弧的超出将是这两个弧长度之间的差，即：2π/3 - π/2 = (4π - 3π)/6 = π/6。这个超出代表了120度弧比90度弧长多少。理解弧的超出在工程和建筑等应用中至关重要，因为精确的测量是必不可少的。例如，在设计曲面结构时，工程师必须考虑弧的超出，以确保使用的材料能够承受施加在它们上的力量。此外，在导航和天文学中，当计算地球表面两点之间的距离时，弧的超出变得尤为重要，尤其是在使用球面模型时。此外，弧的超出也可以与微积分中的概念联系起来，特别是在处理计算曲线长度的积分时。通过理解如何计算弧的超出，学生和专业人士可以将这一知识应用于现实世界的问题，从而增强他们的分析能力和数学推理。总之，弧的超出是几何学中的一个基本概念，它超越了理论数学，延伸到各个学科的实际应用中。通过掌握这一思想，个人可以更深刻地欣赏圆周运动的复杂性以及角度和弧长之间的关系。在我们继续探索几何学的迷人世界时，弧的超出无疑将继续成为进一步研究和应用的重要主题。