orthogonal; cross-out; perpendicularity

简明释义

正交

英英释义

例句

1.The concept of perpendicularity (垂直性) is essential in setting up a proper coordinate system.

在建立适当的坐标系时，垂直性（perpendicularity）的概念是必不可少的。

2.In geometry, two lines that are orthogonal (正交的) to each other intersect at a right angle.

在几何学中，两条互为正交的（orthogonal）直线相交于一个直角。

3.During the meeting, I had to cross-out (划掉) several items from the agenda due to time constraints.

在会议期间，由于时间限制，我不得不从议程中划掉（cross-out）几个项目。

4.When creating a flowchart, it's important to cross-out (划掉) any steps that are no longer relevant.

在制作流程图时，重要的是要划掉（cross-out）任何不再相关的步骤。

5.In data analysis, we often treat independent variables as orthogonal (正交的) to avoid multicollinearity.

在数据分析中，我们通常将自变量视为正交的（orthogonal），以避免多重共线性。

作文

In the realm of mathematics and geometry, the concepts of orthogonal (正交), cross-out (划去), and perpendicularity (垂直性) play significant roles in understanding the relationships between different entities. These terms are not just limited to theoretical applications but extend their relevance into various fields including physics, engineering, and computer science. Understanding these terms deeply can enhance one’s analytical skills and problem-solving abilities.To begin with, the term orthogonal refers to the concept of right angles or perpendicular vectors in a multi-dimensional space. When two vectors are orthogonal, it means that they intersect at a right angle, which is crucial in vector mathematics. This property is particularly useful in fields such as linear algebra where orthogonality is employed to simplify complex calculations. For example, in computer graphics, the use of orthogonal projections helps in rendering images accurately by maintaining the correct angles and dimensions.Next, we have the term cross-out, which literally means to draw a line through something to indicate it should be ignored or eliminated. In mathematical contexts, cross-out can be seen in the process of solving equations where certain terms are crossed out to simplify the expression. This technique is essential for clarity and efficiency in calculations, allowing mathematicians and students alike to focus on the most relevant parts of a problem. The act of cross-out embodies the process of refining ideas and eliminating distractions, which is applicable not only in math but also in everyday decision-making.Finally, perpendicularity is a geometric principle that describes the relationship between two lines or planes that meet at a right angle. When two lines are perpendicular, they create a unique intersection that is often utilized in architectural design and construction. This concept ensures stability and balance in structures, making it a fundamental aspect of engineering. The idea of perpendicularity extends beyond physical structures; it can also represent the alignment of ideas or concepts in a more abstract sense, emphasizing the importance of coherence and logical structure in arguments or theories.In conclusion, the terms orthogonal, cross-out, and perpendicularity are integral to various disciplines, providing a framework for understanding complex relationships. Mastering these concepts not only enhances one’s mathematical prowess but also fosters critical thinking and clarity in communication. By applying these principles in both academic and practical scenarios, individuals can improve their analytical skills and contribute more effectively to their fields of interest. Ultimately, the ability to grasp such foundational concepts will pave the way for deeper insights and innovations in an increasingly complex world.

在数学和几何的领域中，orthogonal（正交）、cross-out（划去）和perpendicularity（垂直性）这几个概念在理解不同实体之间的关系时发挥着重要作用。这些术语不仅限于理论应用，还扩展到物理学、工程学和计算机科学等多个领域。深入理解这些术语可以增强一个人的分析能力和解决问题的能力。首先，orthogonal这个术语指的是在多维空间中直角或垂直向量的概念。当两个向量是orthogonal时，意味着它们在一个直角处相交，这在向量数学中至关重要。这个特性在如线性代数等领域中特别有用，因为正交性被用于简化复杂的计算。例如，在计算机图形学中，使用orthogonal投影有助于准确渲染图像，保持正确的角度和尺寸。接下来是cross-out这个术语，它字面意思是通过某物划一条线，以表明它应该被忽略或消除。在数学上下文中，cross-out可以在解方程的过程中看到，其中某些项被crossed out以简化表达式。这种技术对于计算的清晰性和效率至关重要，使数学家和学生能够集中注意力于问题的最相关部分。cross-out的行为体现了提炼思想和消除干扰的过程，这不仅适用于数学，也适用于日常决策。最后，perpendicularity是一个几何原理，描述了两条线或平面在直角相遇的关系。当两条线是perpendicular时，它们会创建一个独特的交点，这通常在建筑设计和施工中得以应用。这个概念确保了结构的稳定和平衡，使其成为工程学的基本方面。perpendicularity的概念超越了物理结构；它还可以代表思想或概念在更抽象意义上的对齐，强调论点或理论中连贯性和逻辑结构的重要性。总之，orthogonal、cross-out和perpendicularity这些术语在各个学科中都是不可或缺的，提供了理解复杂关系的框架。掌握这些概念不仅增强一个人的数学能力，还促进批判性思维和沟通的清晰度。通过在学术和实践场景中应用这些原则，个人可以提高他们的分析能力，更有效地为他们感兴趣的领域做出贡献。最终，掌握这些基础概念的能力将为在日益复杂的世界中获得更深刻的见解和创新铺平道路。