circumscribed circle

简明释义

外接圆

英英释义

例句

1.In a right triangle, the hypotenuse serves as the diameter of the circumscribed circle 外接圆.

在直角三角形中，斜边作为circumscribed circle 外接圆的直径。

2.The circumscribed circle 外接圆 of a polygon is the smallest circle that can encompass all its vertices.

多边形的circumscribed circle 外接圆是可以包围所有顶点的最小圆。

3.The center of the circumscribed circle 外接圆 is called the circumcenter.

circumscribed circle 外接圆的中心称为外心。

4.In geometry class, we learned how to find the radius of a circumscribed circle 外接圆 around a triangle.

在几何课上，我们学习了如何找到三角形周围的circumscribed circle 外接圆的半径。

5.To construct the circumscribed circle 外接圆, you need to find the perpendicular bisectors of the sides of the triangle.

要构建circumscribed circle 外接圆，您需要找到三角形边的垂直平分线。

作文

In the study of geometry, one of the fascinating concepts is the circumscribed circle, which is defined as a circle that passes through all the vertices of a polygon. This particular circle is significant because it helps in understanding various properties of polygons, especially triangles. The circumscribed circle is not only a theoretical construct but also has practical applications in various fields such as engineering, architecture, and computer graphics.To illustrate the concept, let's consider a triangle. For any given triangle, there exists a unique circumscribed circle. The center of this circle, known as the circumcenter, is the point where the perpendicular bisectors of the sides of the triangle intersect. This point can be located inside the triangle for acute triangles, on the triangle for right triangles, and outside the triangle for obtuse triangles. Understanding the location of the circumcenter is crucial for many geometric constructions and proofs.The radius of the circumscribed circle is called the circumradius, which is the distance from the circumcenter to any of the triangle's vertices. The circumradius can be calculated using various formulas depending on the type of triangle. For instance, in an equilateral triangle, the circumradius is simply the length of a side divided by the square root of three. This relationship highlights the beauty of geometry, where simple ratios and relationships can lead to profound insights about shapes.Moreover, the circumscribed circle has interesting properties that extend beyond triangles. For example, in regular polygons, all vertices lie on the same circumscribed circle, making it easier to calculate their area and other attributes. This characteristic allows mathematicians and scientists to derive formulas that apply to all regular polygons, further emphasizing the importance of the circumscribed circle in geometry.In real-world applications, understanding the circumscribed circle can be immensely beneficial. Engineers often use this concept when designing structures that require circular elements, ensuring that forces are distributed evenly across all points. In computer graphics, the circumscribed circle can help in rendering shapes accurately, allowing for more realistic animations and designs. Thus, the concept transcends pure mathematics and finds its way into practical applications that affect our daily lives.In conclusion, the circumscribed circle is a fundamental concept in geometry that connects various mathematical principles and has numerous applications in the real world. By understanding this concept, we gain insights not only into the properties of polygons but also into the practical implications of geometric principles. Whether it is in the classroom or in professional practice, the circumscribed circle serves as a vital tool for anyone interested in the field of mathematics and its applications.

在几何学的研究中，一个迷人的概念是外接圆，它被定义为一个通过多边形所有顶点的圆。这个特定的圆是重要的，因为它有助于理解多边形的各种属性，尤其是三角形。外接圆不仅是一个理论构造，而且在工程、建筑和计算机图形等多个领域具有实际应用。为了说明这个概念，让我们考虑一个三角形。对于任何给定的三角形，都存在一个独特的外接圆。这个圆的中心被称为外心，是三角形各边的垂直平分线交汇的点。对于锐角三角形，这个点可以位于三角形内部；对于直角三角形，它位于三角形上；而对于钝角三角形，它则位于三角形外部。理解外心的位置对于许多几何构造和证明至关重要。外接圆的半径称为外接半径，它是从外心到三角形任何一个顶点的距离。外接半径可以根据三角形的类型使用不同的公式进行计算。例如，在等边三角形中，外接半径只是边长除以根号三。这种关系突显了几何的美丽，在简单的比率和关系中可以引出对形状的深刻见解。此外，外接圆还有一些超出三角形的有趣属性。例如，在正多边形中，所有顶点都位于同一个外接圆上，这使得计算它们的面积和其他属性变得更加容易。这一特性使得数学家和科学家能够推导出适用于所有正多边形的公式，进一步强调了外接圆在几何学中的重要性。在现实世界的应用中，理解外接圆可能非常有益。工程师在设计需要圆形元素的结构时，常常使用这个概念，以确保力在所有点均匀分布。在计算机图形学中，外接圆可以帮助准确渲染形状，从而实现更逼真的动画和设计。因此，这个概念超越了纯数学，并找到了影响我们日常生活的实际应用。总之，外接圆是几何学中的一个基础概念，它连接了各种数学原理，并在现实世界中有众多应用。通过理解这一概念，我们不仅获得了对多边形属性的洞察，还了解了几何原理的实际意义。无论是在课堂上还是在专业实践中，外接圆都是任何对数学及其应用感兴趣的人必不可少的工具。