rectangular coordinate

简明释义

直角坐标

英英释义

例句

1.Engineers often rely on rectangular coordinate 直角坐标 systems for designing mechanical parts.

工程师们常常依赖直角坐标系统来设计机械零件。

2.In computer graphics, rectangular coordinate 直角坐标 systems are crucial for rendering images accurately.

在计算机图形学中，直角坐标系统对于准确渲染图像至关重要。

3.In mathematics, we often use rectangular coordinate 直角坐标 systems to plot points on a graph.

在数学中，我们常常使用直角坐标系统在图表上绘制点。

4.When converting from polar to rectangular coordinate 直角坐标, the formulas x = r * cos(θ) and y = r * sin(θ) are used.

从极坐标转换为直角坐标时，使用公式x = r * cos(θ)和y = r * sin(θ)。

5.The location of a point can be described using rectangular coordinate 直角坐标 values (x, y).

一个点的位置可以用直角坐标值（x，y）来描述。

作文

In the realm of mathematics and physics, understanding the concept of rectangular coordinate is fundamental. A rectangular coordinate system, also known as Cartesian coordinates, is a method for defining the position of points in a two-dimensional or three-dimensional space using numerical values. This system employs two or three perpendicular axes to represent dimensions, typically labeled as x, y, and z. The intersection point of these axes is called the origin, denoted as (0, 0) in two dimensions and (0, 0, 0) in three dimensions. To comprehend how rectangular coordinates work, consider a simple example: plotting a point on a two-dimensional plane. If we want to plot the point (3, 4), we start at the origin. We move three units along the x-axis (horizontal direction) and then four units up along the y-axis (vertical direction). The point where we end up is (3, 4). This straightforward method allows us to visualize and locate points easily, making it an invaluable tool in various fields such as engineering, computer graphics, and navigation.Moreover, the rectangular coordinate system extends beyond just two dimensions. In three-dimensional space, we introduce a z-axis perpendicular to both the x and y axes. For instance, if we have a point represented as (2, 3, 5), we would first move two units along the x-axis, three units along the y-axis, and then five units up along the z-axis. This ability to represent points in three dimensions opens up a new world of possibilities, especially in fields like architecture and physics, where spatial relationships are crucial.Understanding the mathematical equations that govern rectangular coordinates is also essential. For instance, the equation of a line in a two-dimensional rectangular coordinate system can be expressed in the slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept. This equation allows us to determine the relationship between x and y values, helping us understand how they interact within the coordinate system.In addition to lines, rectangular coordinates can also be used to express more complex shapes, such as circles and parabolas. The equation of a circle centered at the origin with a radius r can be written as x² + y² = r². This equation highlights the beauty and symmetry of circles within the rectangular coordinate framework.Furthermore, the application of rectangular coordinates is not limited to theoretical mathematics. In real-world scenarios, engineers use this system to design bridges, buildings, and other structures. Computer scientists utilize rectangular coordinates in graphics programming to create animations and render images accurately. Even in navigation systems, rectangular coordinates help determine precise locations on maps, enhancing our ability to explore and travel.In conclusion, the concept of rectangular coordinates is a cornerstone of mathematics and science. Its simplicity and effectiveness in representing points in space make it an indispensable tool across various disciplines. By mastering rectangular coordinates, one enhances their problem-solving skills and gains a deeper appreciation for the interconnectedness of the mathematical world. Whether you are a student, an engineer, or simply a curious mind, understanding rectangular coordinates will undoubtedly enrich your knowledge and capabilities in numerous ways.

在数学和物理的领域中，理解矩形坐标的概念是基础。矩形坐标系统，也称为笛卡尔坐标，是一种通过数字值定义二维或三维空间中点位置的方法。该系统使用两个或三个垂直轴来表示维度，通常标记为x、y和z。这些轴的交点称为原点，在二维中表示为(0, 0)，在三维中表示为(0, 0, 0)。为了理解矩形坐标的工作原理，考虑一个简单的例子：在二维平面上绘制一个点。如果我们想绘制点(3, 4)，我们从原点开始。我们沿x轴（水平方向）移动三单位，然后沿y轴（垂直方向）向上移动四单位。我们最终到达的点是(3, 4)。这种简单的方法使我们能够轻松可视化和定位点，使其成为工程、计算机图形和导航等各个领域中的宝贵工具。此外，矩形坐标系统不仅限于二维。在三维空间中，我们引入一个与x轴和y轴垂直的z轴。例如，如果我们有一个点表示为(2, 3, 5)，我们首先沿x轴移动两单位，沿y轴移动三单位，然后沿z轴向上移动五单位。这种在三维中表示点的能力打开了新的可能性，特别是在建筑和物理等领域，空间关系至关重要。理解支配矩形坐标的数学方程也是至关重要的。例如，在二维矩形坐标系统中，直线的方程可以用斜截式表示：y = mx + b，其中m代表斜率，b代表y截距。这个方程使我们能够确定x和y值之间的关系，帮助我们理解它们在坐标系统中的相互作用。除了直线，矩形坐标还可以用来表达更复杂的形状，例如圆和抛物线。以原点为中心、半径为r的圆的方程可以写成x² + y² = r²。这个方程突显了圆在矩形坐标框架内的美丽和对称。此外，矩形坐标的应用不仅限于理论数学。在现实世界场景中，工程师利用该系统设计桥梁、建筑和其他结构。计算机科学家在图形编程中利用矩形坐标准确地创建动画和渲染图像。甚至在导航系统中，矩形坐标帮助确定地图上的精确位置，增强了我们探索和旅行的能力。总之，矩形坐标的概念是数学和科学的基石。它在空间中表示点的简单性和有效性使其成为各个学科中不可或缺的工具。通过掌握矩形坐标，人们增强了解决问题的能力，并对数学世界的相互联系有更深刻的理解。无论你是学生、工程师，还是仅仅是一个好奇的人，理解矩形坐标无疑会以多种方式丰富你的知识和能力。