describing circle

简明释义

滚动圆

英英释义

例句

1.During the art lesson, we created a describing circle to frame our drawings.

在美术课上，我们创建了一个描述圆来框住我们的画作。

2.In geometry class, we learned about the properties of a describing circle.

在几何课上，我们学习了关于描述圆的性质。

3.The mathematician explained how to find the radius of a describing circle.

数学家解释了如何找到描述圆的半径。

4.In the software simulation, the describing circle represented the area of influence.

在软件模拟中，描述圆代表了影响范围。

5.The engineer used a describing circle to ensure the design was accurate.

工程师使用描述圆来确保设计的准确性。

作文

The concept of a describing circle is essential in geometry, particularly when discussing the properties of polygons. A describing circle is defined as a circle that passes through all the vertices of a polygon. This means that every corner or vertex of the polygon touches the circumference of the circle. Understanding this concept helps in various applications, including construction, design, and even computer graphics. To illustrate the significance of a describing circle, let us consider a triangle. Every triangle has a unique describing circle, known as the circumcircle. The center of this circle is called the circumcenter, which is the point where the perpendicular bisectors of the triangle's sides intersect. The radius of the circumcircle can be calculated using the lengths of the triangle's sides and the area of the triangle. This relationship is not only fascinating but also useful in solving various problems in geometry.Moreover, the describing circle plays a crucial role in determining the nature of the polygon. For instance, if a polygon can be inscribed in a circle, it is said to be a cyclic polygon. All cyclic polygons have their vertices lying on the circumference of their respective describing circles. This property allows mathematicians and engineers to derive several important theorems and formulas. One such theorem is the fact that the opposite angles of a cyclic quadrilateral are supplementary, meaning they add up to 180 degrees.In addition to its theoretical importance, the describing circle has practical applications. In fields such as architecture and engineering, understanding how to construct a describing circle can help in creating structures that are aesthetically pleasing and structurally sound. When designing a circular building or a roundabout, engineers often use the principles of describing circles to ensure that the design is both functional and visually appealing.Furthermore, in computer graphics, the describing circle concept is used in algorithms for rendering shapes and animations. When creating complex shapes, programmers often rely on the properties of describing circles to simplify calculations and improve performance. By understanding how to manipulate these circles, artists and developers can create stunning visual effects and realistic animations.In conclusion, the concept of a describing circle is not only fundamental in the study of geometry but also has wide-ranging applications in various fields. Whether you are a student learning about polygons, an engineer designing a new structure, or a programmer creating graphics, grasping the idea of a describing circle is invaluable. It connects theoretical mathematics with real-world applications, showcasing the beauty and utility of geometry in our daily lives. Therefore, mastering the concept of a describing circle will undoubtedly enhance one's understanding of both mathematical principles and their practical implications.

在几何学中，描述圆的概念至关重要，特别是在讨论多边形的性质时。描述圆被定义为一个通过多边形所有顶点的圆。这意味着多边形的每个角或顶点都接触到圆的周长。理解这个概念有助于在建筑、设计甚至计算机图形学等各种应用中。为了说明描述圆的重要性，让我们考虑一个三角形。每个三角形都有一个独特的描述圆，称为外接圆。这个圆的中心称为外心，它是三角形边的垂直平分线交汇的点。外接圆的半径可以使用三角形的边长和面积来计算。这种关系不仅令人着迷，而且在解决几何问题时也很有用。此外，描述圆在确定多边形的性质方面起着关键作用。例如，如果一个多边形可以被内切于一个圆中，那么它被称为循环多边形。所有循环多边形的顶点都位于各自的描述圆的周长上。这个性质使数学家和工程师能够推导出几个重要的定理和公式。一个这样的定理是，循环四边形的对角相加为180度，意味着它们是互补的。除了理论上的重要性，描述圆还有实际应用。在建筑和工程等领域，理解如何构造描述圆可以帮助创建既美观又结构坚固的建筑。当设计一个圆形建筑或环形交叉口时，工程师通常使用描述圆的原理来确保设计既功能性又视觉吸引力。此外，在计算机图形学中，描述圆的概念用于渲染形状和动画的算法。当创建复杂形状时，程序员通常依赖描述圆的属性来简化计算并提高性能。通过理解如何操纵这些圆，艺术家和开发者可以创造出惊人的视觉效果和现实的动画。总之，描述圆的概念不仅在几何学的研究中是基础，而且在各个领域有广泛的应用。无论你是学习多边形的学生、设计新结构的工程师，还是创建图形的程序员，掌握描述圆的概念都是无价的。它将理论数学与现实世界的应用联系起来，展示了几何在我们日常生活中的美丽和实用性。因此，掌握描述圆的概念无疑会增强人们对数学原理及其实际意义的理解。