circumcircle

简明释义

英[ˈsɜrkəmˌsɜrkl]美[ˈsɜrkəmˌsɜrkl]

n. [数] 外接圆

英英释义

单词用法

同义词

反义词

例句

1.The roundness of grit's projection was assessed by minimum circumcircle method.

以最小外接圆法评定了金刚石颗粒投影的圆度。

2.An improved algorithm of node refinement scheme called endpoint triangle's circumcircle method (ETCM) is proposed, which has a linear time complexity.

本文提出了一种改进的细分嵌入算法——端点外接圆法(ETCM)，该算法具有线性时间复杂度。

3.An improved algorithm of node refinement scheme called endpoint triangle's circumcircle method (ETCM) is proposed, which has a linear time complexity.

本文提出了一种改进的细分嵌入算法——端点外接圆法(ETCM)，该算法具有线性时间复杂度。

4.When constructing a triangle, the circumcircle can help in determining if the triangle is acute, right, or obtuse.

在构造三角形时，外接圆可以帮助确定三角形是锐角、直角还是钝角。

5.In geometry, the circumcircle of a triangle is the unique circle that passes through all three vertices.

在几何中，三角形的外接圆是唯一一个通过所有三个顶点的圆。

6.For any triangle, the circumcircle can be drawn using only a compass and straightedge.

对于任何三角形，外接圆都可以仅使用圆规和直尺绘制。

7.The center of the circumcircle is called the circumcenter, which is the point where the perpendicular bisectors of the sides meet.

外接圆的中心称为外心，是各边的垂直平分线交汇的点。

8.To find the radius of the circumcircle, you can use the formula R = abc / (4K), where K is the area of the triangle.

要找到外接圆的半径，可以使用公式 R = abc / (4K)，其中 K 是三角形的面积。

作文

In the study of geometry, one of the fascinating concepts is the circumcircle, which refers to the circle that passes through all the vertices of a polygon. This concept is particularly significant when considering triangles, as every triangle has a unique circumcircle. The center of this circle is known as the circumcenter, and it is the point where the perpendicular bisectors of the triangle's sides intersect. Understanding the properties of the circumcircle can greatly enhance our appreciation of geometric relationships.To illustrate the importance of the circumcircle, consider a triangle ABC. By constructing the circumcircle, we can observe how the circumcenter relates to the triangle's angles and sides. The radius of the circumcircle is equal to the distance from the circumcenter to any of the triangle's vertices. This radius can be calculated using various formulas, depending on the triangle's dimensions. For instance, in a right triangle, the circumradius is half the length of the hypotenuse.The circumcircle also plays a crucial role in various theorems and proofs in geometry. One such theorem is the circumcircle theorem, which states that if a triangle is inscribed in a circle, then the angle subtended by any side at the circumference is equal to the angle subtended at the center. This theorem not only helps in solving problems related to angles but also provides insights into cyclic quadrilaterals, where all four vertices lie on a single circumcircle.Additionally, the concept of the circumcircle extends beyond triangles to other polygons. For example, a regular polygon can also have a circumcircle that passes through all its vertices. The radius of this circle is consistent across all vertices, making it easier to analyze the polygon's symmetry and properties. Understanding how to construct and utilize the circumcircle of various shapes can lead to deeper insights in both theoretical and applied mathematics.In practical applications, the circumcircle can be used in fields such as computer graphics, architecture, and engineering. For instance, when designing structures, architects often need to understand the spatial relationships between different components. The circumcircle can help visualize these relationships, ensuring that designs are both aesthetically pleasing and structurally sound.In conclusion, the circumcircle is more than just a geometric concept; it is a vital tool for understanding the relationships between different shapes and their properties. Whether we are studying triangles or more complex polygons, the ability to construct and analyze the circumcircle opens up a world of possibilities in geometry. As we continue to explore this field, the significance of the circumcircle will undoubtedly remain a cornerstone of geometric study and application.

在几何学的研究中，一个引人入胜的概念是外接圆，指的是通过多边形所有顶点的圆。这个概念在考虑三角形时尤为重要，因为每个三角形都有一个独特的外接圆。这个圆的中心称为外心，是三角形边的垂直平分线交点。理解外接圆的性质可以大大增强我们对几何关系的欣赏。为了说明外接圆的重要性，考虑一个三角形ABC。通过构造外接圆，我们可以观察外心与三角形的角和边之间的关系。外接圆的半径等于外心到三角形任一顶点的距离。根据三角形的尺寸，这个半径可以使用各种公式进行计算。例如，在直角三角形中，外接半径是斜边长度的一半。外接圆在几何中的各种定理和证明中也发挥着至关重要的作用。一个这样的定理是外接圆定理，它指出如果一个三角形被描绘在一个圆内，则任一边在圆周上的弦所对的角等于在圆心所对的角。这个定理不仅有助于解决与角度相关的问题，还提供了对循环四边形的见解，其中所有四个顶点都位于同一个外接圆上。此外，外接圆的概念不仅限于三角形，还扩展到其他多边形。例如，正多边形也可以有一个外接圆，该圆通过所有顶点。这个圆的半径在所有顶点之间是一致的，使得分析多边形的对称性和性质变得更加容易。理解如何构造和利用各种形状的外接圆可以带来更深入的理论和应用数学见解。在实际应用中，外接圆可以用于计算机图形学、建筑学和工程等领域。例如，在设计结构时，建筑师通常需要理解不同组件之间的空间关系。外接圆可以帮助可视化这些关系，确保设计既美观又结构合理。总之，外接圆不仅仅是一个几何概念；它是理解不同形状及其性质之间关系的重要工具。无论我们是在研究三角形还是更复杂的多边形，构建和分析外接圆的能力为几何学的可能性打开了一个全新的世界。随着我们继续探索这个领域，外接圆的重要性无疑将继续成为几何研究和应用的基石。