principal dimensions

简明释义

知尺寸

英英释义

例句

1.The principal dimensions of the aircraft were optimized to enhance its aerodynamic performance.

飞机的主要尺寸经过优化，以提高其气动性能。

2.The engineer calculated the principal dimensions of the bridge to ensure it could support the expected load.

工程师计算了桥梁的主要尺寸以确保它能够承受预期的负载。

3.In architecture, understanding the principal dimensions of a building is crucial for design and functionality.

在建筑学中，理解建筑的主要尺寸对于设计和功能至关重要。

4.The designer presented the principal dimensions of the furniture pieces during the client meeting.

设计师在客户会议上展示了家具的主要尺寸。

5.When modeling the new product, we need to define the principal dimensions accurately to avoid manufacturing errors.

在建模新产品时，我们需要准确地定义主要尺寸以避免制造错误。

作文

In the study of various fields such as physics, engineering, and mathematics, understanding the concept of principal dimensions is essential. These dimensions refer to the fundamental measures that define the properties and behaviors of objects or systems. For instance, in mechanics, the principal dimensions can include length, mass, and time, which are crucial for analyzing motion and forces. When we delve into structural engineering, the principal dimensions of materials become even more critical. The strength, elasticity, and thermal expansion of materials can be characterized by their principal dimensions. Engineers must account for these dimensions when designing structures to ensure safety and stability. Moreover, in the realm of fluid dynamics, the principal dimensions play a significant role in characterizing fluid flow. Parameters such as velocity, pressure, and density are all considered principal dimensions that affect how fluids behave under various conditions. Understanding these dimensions allows engineers to create efficient systems for water supply, air conditioning, and even aerodynamics in vehicles. In mathematics, particularly in linear algebra, we often encounter the term principal dimensions in the context of matrices and transformations. The eigenvalues and eigenvectors of a matrix can be seen as principal dimensions that provide insight into the behavior of linear transformations. By analyzing these dimensions, mathematicians can determine how a system will evolve over time, which is particularly useful in fields such as computer graphics and data analysis. Furthermore, in the field of statistics, the concept of principal dimensions manifests in techniques such as Principal Component Analysis (PCA). PCA is a method used to reduce the dimensionality of data while preserving as much variance as possible. The resulting components can be thought of as the principal dimensions that capture the most significant patterns within the dataset. This technique is widely used in machine learning and data mining, allowing researchers to uncover insights from complex datasets. In conclusion, the term principal dimensions encompasses a variety of fundamental measures across different disciplines. Whether in engineering, physics, mathematics, or statistics, these dimensions provide a framework for understanding the properties and behaviors of various systems. Mastering the concept of principal dimensions not only enhances our comprehension of scientific principles but also equips us with the tools necessary to innovate and solve complex problems in our world. As we continue to explore and apply these dimensions in various contexts, we unlock new possibilities for advancement and discovery.

在物理学、工程学和数学等多个领域，理解主维度的概念至关重要。这些维度指的是定义物体或系统属性和行为的基本测量。例如，在力学中，主维度可以包括长度、质量和时间，这些都是分析运动和力的关键因素。当我们深入结构工程时，材料的主维度变得更加重要。材料的强度、弹性和热膨胀都可以通过其主维度来表征。工程师在设计结构时必须考虑这些维度，以确保安全和稳定。此外，在流体动力学领域，主维度在特征化流体流动方面也发挥着重要作用。速度、压力和密度等参数都是影响流体在各种条件下行为的主维度。理解这些维度使工程师能够创建高效的供水、空调系统，甚至是车辆的空气动力学。在数学中，特别是在线性代数中，我们常常在矩阵和变换的上下文中遇到主维度这个术语。矩阵的特征值和特征向量可以看作是提供线性变换行为见解的主维度。通过分析这些维度，数学家可以确定一个系统随时间如何演变，这在计算机图形学和数据分析等领域尤其有用。此外，在统计学领域，主维度的概念体现在诸如主成分分析（PCA）等技术中。PCA是一种用于减少数据维度的方法，同时尽可能保留方差。结果组件可以被视为捕捉数据集中最显著模式的主维度。这一技术在机器学习和数据挖掘中广泛应用，使研究人员能从复杂的数据集中发现洞察。总之，主维度一词涵盖了不同学科中的多种基本测量。无论是在工程、物理、数学还是统计学中，这些维度为理解各种系统的属性和行为提供了框架。掌握主维度的概念不仅增强了我们对科学原理的理解，还为我们提供了解决复杂问题所需的工具。随着我们继续在各种背景下探索和应用这些维度，我们为进步和发现开启了新的可能性。