polar angle

简明释义

极角

英英释义

例句

1.In spherical coordinates, the position of a point is defined by its radial distance, azimuthal angle, and polar angle（极角）.

在球坐标中，一个点的位置由其径向距离、方位角和极角（极角）定义。

2.To calculate the area on a sphere, you need to know the polar angle（极角） and the azimuthal angle.

要计算球面上的面积，你需要知道极角（极角）和方位角。

3.The polar angle（极角）can be measured from the positive z-axis down to the point in three-dimensional space.

从正z轴到三维空间中某点的测量可以用极角（极角）表示。

4.When plotting data in spherical coordinates, it is essential to correctly set the polar angle（极角）.

在球坐标中绘制数据时，正确设置极角（极角）是至关重要的。

5.In physics, the polar angle（极角） is often used to describe the orientation of particles in spherical systems.

在物理学中，极角（极角）常用于描述粒子在球形系统中的方向。

作文

In the realm of mathematics and physics, understanding various angles is crucial for solving problems related to geometry and trigonometry. One such angle that plays a significant role in spherical coordinate systems is the polar angle. The polar angle is defined as the angle between the positive z-axis and the line connecting the origin to a point in three-dimensional space. It is an essential component when converting from Cartesian coordinates (x, y, z) to spherical coordinates (r, θ, φ). Here, 'r' represents the radius or the distance from the origin, 'θ' is the azimuthal angle, and 'φ' is the polar angle.To grasp the concept of the polar angle, it is helpful to visualize it in a three-dimensional context. Imagine a sphere centered at the origin of a coordinate system. Any point on the surface of this sphere can be described using spherical coordinates. The polar angle indicates how far up or down the point is from the horizontal plane (the xy-plane). When the polar angle is zero, the point lies directly above the origin along the positive z-axis. As the polar angle increases towards 90 degrees, the point moves downward toward the equatorial plane of the sphere. At 90 degrees, the point lies in the xy-plane, and as the polar angle exceeds 90 degrees, the point continues downward into the negative z-axis.The significance of the polar angle extends beyond mere geometric representation; it also plays a vital role in various physical applications. For instance, in physics, the polar angle is used in the analysis of spherical harmonics, which are functions that arise in solutions to problems involving angular momentum in quantum mechanics. In this context, the polar angle helps define the orientation of particles and their wave functions, leading to a deeper understanding of atomic structures and behaviors.Moreover, the polar angle is frequently encountered in fields such as computer graphics, where it aids in rendering three-dimensional objects. By manipulating the polar angle, artists and developers can achieve different perspectives and visual effects, enhancing the overall experience of digital environments.In conclusion, the polar angle is a fundamental concept in both mathematics and physics, serving as a bridge between two-dimensional and three-dimensional representations. Its importance cannot be overstated, as it not only facilitates the conversion of coordinates but also enriches our understanding of physical phenomena and enhances our ability to create realistic digital models. By mastering the concept of the polar angle, students and professionals alike can unlock new avenues of exploration in various scientific and artistic fields.

在数学和物理的领域中，理解各种角度对于解决与几何和三角学相关的问题至关重要。其中一个在球坐标系统中发挥重要作用的角度是极角。极角被定义为正z轴与连接原点到三维空间中某一点的直线之间的角度。当从笛卡尔坐标（x，y，z）转换为球坐标（r，θ，φ）时，它是一个重要组成部分。在这里，'r'表示从原点的半径或距离，'θ'是方位角，而'φ'是极角。要掌握极角的概念，想象一下在坐标系统原点处的一个球体是很有帮助的。这个球体表面上的任何点都可以用球坐标描述。极角表示该点相对于水平面（xy平面）的上下位置。当极角为零时，该点直接位于正z轴上方。随着极角向90度增加，该点向下移动到球体的赤道平面。当极角达到90度时，该点位于xy平面，而当极角超过90度时，该点继续向下进入负z轴。极角的重要性超出了简单的几何表示；它在各种物理应用中也起着重要作用。例如，在物理学中，极角用于分析球谐函数，这些函数出现在涉及量子力学中角动量问题的解中。在这种情况下，极角有助于定义粒子的方向及其波函数，从而更深入地理解原子结构和行为。此外，极角在计算机图形学等领域中也经常遇到，它有助于渲染三维物体。通过操控极角，艺术家和开发者可以实现不同的视角和视觉效果，从而增强数字环境的整体体验。总之，极角是数学和物理中的一个基本概念，它作为二维和三维表示之间的桥梁，其重要性不容小觑，因为它不仅促进了坐标的转换，还丰富了我们对物理现象的理解，并增强了我们创建逼真数字模型的能力。通过掌握极角的概念，学生和专业人士可以在各种科学和艺术领域开启新的探索途径。