geometric cross section

简明释义

几何截面

英英释义

例句

1.To visualize the internal features, we examined the geometric cross section of the product.

为了可视化内部特征，我们检查了产品的几何截面。

2.The geometric cross section of the cylinder is essential for calculating its volume.

圆柱的几何截面对于计算其体积至关重要。

3.In this design project, we need to create a geometric cross section that accurately represents the dimensions of the structure.

在这个设计项目中，我们需要创建一个准确表示结构尺寸的几何截面。

4.The architect provided a detailed drawing of the geometric cross section of the building for the construction team.

建筑师为施工团队提供了建筑的几何截面详细图纸。

5.The engineer analyzed the geometric cross section of the beam to determine its load-bearing capacity.

工程师分析了梁的几何截面以确定其承载能力。

作文

In the study of mathematics and engineering, the term geometric cross section refers to the two-dimensional shape obtained by cutting through a three-dimensional object. This concept is fundamental in various fields, including physics, architecture, and material science, as it allows us to analyze and understand the properties of complex structures. By examining the geometric cross section of an object, we can gain insights into its volume, surface area, and structural integrity. For example, consider a cylinder. When we take a horizontal slice through the cylinder, the geometric cross section will be a circle. If we were to slice it vertically, the resulting geometric cross section would be a rectangle. These cross sections provide valuable information about the shape and dimensions of the cylinder, which can be crucial for applications such as designing pipes or storage tanks. In architecture, understanding the geometric cross section of a building can help architects visualize how different elements interact with one another. For instance, the cross section of a beam can reveal how much load it can bear, which is essential for ensuring safety and stability in construction. Similarly, in the field of material science, analyzing the geometric cross section of materials can lead to discoveries about their strength, flexibility, and resistance to various forces. Moreover, the concept of geometric cross section extends beyond physical objects; it can also apply to abstract mathematical shapes. In calculus, for instance, we often calculate the area of a geometric cross section to determine the volume of solids of revolution. This is done by integrating the area of the cross sections along the axis of rotation, showcasing the interplay between geometry and calculus. In conclusion, the geometric cross section is a crucial concept that bridges various disciplines, providing a means to simplify and analyze complex three-dimensional forms. Whether in engineering, architecture, or mathematics, understanding the implications of a geometric cross section allows professionals to make informed decisions and designs. As we continue to explore the intricacies of shapes and structures, the importance of this concept will only grow, highlighting its relevance in both theoretical and practical applications.

在数学和工程学的研究中，术语几何截面指的是通过三维物体切割所得到的二维形状。这个概念在物理学、建筑学和材料科学等多个领域中都是基础，因为它使我们能够分析和理解复杂结构的特性。通过检查一个物体的几何截面，我们可以深入了解其体积、表面积和结构完整性。例如，考虑一个圆柱体。当我们对圆柱体进行水平切割时，几何截面将是一个圆形。如果我们垂直切割，得到的几何截面将是一个矩形。这些截面提供了有关圆柱体形状和尺寸的宝贵信息，这在设计管道或储罐等应用中至关重要。在建筑学中，理解建筑物的几何截面可以帮助建筑师可视化不同元素之间的相互作用。例如，梁的截面可以揭示它能承受多大的负荷，这对确保建筑安全和稳定至关重要。同样，在材料科学领域，分析材料的几何截面可以导致对其强度、柔韧性和抵抗各种力量的发现。此外，几何截面的概念超越了物理对象；它也可以应用于抽象的数学形状。在微积分中，我们经常计算一个几何截面的面积，以确定旋转体的体积。这是通过沿旋转轴积分截面的面积来完成的，展示了几何与微积分之间的相互作用。总之，几何截面是一个重要的概念，它连接了多个学科，为简化和分析复杂的三维形态提供了一种手段。无论是在工程、建筑还是数学领域，理解几何截面的含义使专业人员能够做出明智的决策和设计。随着我们继续探索形状和结构的复杂性，这个概念的重要性只会增加，突显其在理论和实际应用中的相关性。