supplementary arc

简明释义

余弧

英英释义

例句

1.The architect used supplementary arcs in the design to create harmonious curves.

建筑师在设计中使用了补充弧来创造和谐的曲线。

2.In a circle, the supplementary arc can help determine the length of the remaining arc.

在一个圆中，补充弧可以帮助确定剩余弧的长度。

3.In geometry, the angle formed by a supplementary arc is always 180 degrees.

在几何中，由补充弧形成的角度总是180度。

4.The two arcs on the circle are supplementary arcs because they add up to a complete rotation.

圆上的两个弧是补充弧，因为它们加起来形成一个完整的旋转。

5.When designing the track, we need to calculate the supplementary arc to ensure smooth transitions.

在设计轨道时，我们需要计算补充弧以确保平滑过渡。

作文

In the study of geometry, various terms and concepts play a crucial role in understanding the relationships between different shapes and angles. One such term is the supplementary arc, which refers to an arc whose measure, when added to the measure of another arc, equals 180 degrees. This concept is particularly important when analyzing circles and their properties. Understanding supplementary arc can enhance our comprehension of how angles interact within circular figures. To illustrate the significance of the supplementary arc, consider a circle divided into two arcs, A and B. If the measure of arc A is 120 degrees, then the measure of arc B must be 60 degrees for the two arcs to be supplementary. This relationship can be expressed mathematically as: Measure of arc A + Measure of arc B = 180 degrees. Thus, we can conclude that arc B is a supplementary arc to arc A. The concept of supplementary arc is not only limited to theoretical mathematics but also has practical applications in various fields such as engineering, architecture, and physics. For example, in architectural design, understanding the angles created by arches and the corresponding arcs can lead to more aesthetically pleasing and structurally sound buildings. Architects often use the principles of supplementary angles and arcs to ensure that their designs are both functional and visually appealing.Moreover, in the realm of physics, the concept of supplementary arc can be observed in the analysis of rotational motion. When studying the movement of objects in circular paths, it is essential to understand how different angles relate to one another. For instance, if an object moves along a circular path and covers an arc of 90 degrees, the remaining arc that completes the half-circle will be a supplementary arc measuring 90 degrees as well. This understanding aids in predicting the motion and behavior of rotating bodies.Furthermore, the study of supplementary arc can also lead to deeper insights in trigonometry. Trigonometric identities often involve the use of supplementary angles, which can be directly related to the concept of supplementary arc. For example, the sine of an angle and the sine of its supplementary angle have a specific relationship, which can be expressed as: sin(θ) = sin(180° - θ). This relationship is fundamental in solving various mathematical problems involving angles and arcs.In conclusion, the supplementary arc is a vital concept within the field of geometry that extends beyond mere definitions. It enhances our understanding of the relationships between angles, arcs, and their applications in real-world scenarios. By grasping the importance of the supplementary arc, students and professionals alike can apply this knowledge in various disciplines, from mathematics to engineering, ultimately leading to better problem-solving skills and a deeper appreciation for the beauty of geometric relationships.

在几何学的研究中，各种术语和概念在理解不同形状和角度之间的关系方面起着至关重要的作用。一个这样的术语是补充弧，它指的是一个弧的度数与另一个弧的度数相加等于180度的弧。这个概念在分析圆及其属性时尤其重要。理解补充弧可以增强我们对圆形图形中角度如何相互作用的理解。为了说明补充弧的重要性，考虑一个被分成两个弧A和B的圆。如果弧A的度数为120度，那么弧B的度数必须为60度，以使这两个弧成为补充关系。这个关系可以用数学公式表示为：弧A的度数 + 弧B的度数 = 180度。因此，我们可以得出结论，弧B是弧A的补充弧。补充弧的概念不仅限于理论数学，它在工程、建筑和物理等多个领域也有实际应用。例如，在建筑设计中，理解拱门所形成的角度与相应弧的关系，可以导致更具美感和结构稳固的建筑。建筑师常常利用补充角和弧的原理来确保他们的设计既功能性强又视觉上吸引人。此外，在物理学领域，补充弧的概念可以在分析旋转运动时观察到。当研究沿圆形路径移动的物体时，理解不同角度之间的关系是至关重要的。例如，如果一个物体沿圆形路径移动并覆盖了90度的弧，完成半圆的剩余弧将是一个度数为90度的补充弧。这种理解有助于预测旋转物体的运动和行为。此外，补充弧的研究还可以在三角学中带来更深入的见解。三角恒等式通常涉及补充角的使用，这可以直接与补充弧的概念相关联。例如，一个角的正弦值与其补充角的正弦值之间有特定的关系，可以表达为：sin(θ) = sin(180° - θ)。这个关系在解决涉及角度和弧的各种数学问题时是基础性的。总之，补充弧是几何学领域中的一个重要概念，它超越了单纯的定义。它增强了我们对角度、弧及其在现实世界场景中应用的关系的理解。通过掌握补充弧的重要性，学生和专业人士都可以在各个学科中应用这些知识，从数学到工程，最终提高解决问题的能力，并更深刻地欣赏几何关系的美妙。