circumcenter

circumcenter的音标是["sɜːkməʊˌsentə(r)]，基本翻译是圆周中心，速记技巧是“四百”谐音记忆。

circumcenter这个词的词源可以追溯到拉丁语词circus（圆）和center（中心）。它的意思是圆心或圆周上的中心点。

变化形式：在数学中，我们通常用circumcenter来表示圆周上的中心，它是一个单数形式。在英语中，它也可以被写作circumcenter或circle center。

相关单词：

1. center（中心）：这个单词和circumcenter非常接近，都是表示一个物体的中心点。

2. midpoint（中点）：这个单词用来表示线段或图形的中心点。

3. axis（轴）：这个单词用来表示一个几何形状围绕的中心线。

4. pole（极）：这个单词用来表示一个几何形状的极点，也就是一个特定方向上的中心点。

5. focus（焦点）：这个单词用来表示一个光学系统的中心点，也就是光线聚焦的地方。

6. radius（半径）：这个单词用来表示一个圆或球体的半径，也就是圆或球体的中心点到边缘的距离。

7. circumradius（圆半径）：这个单词用来表示一个圆的circumcenter到其边缘的距离。

8. symmetry center（对称中心）：这个单词用来表示一个对称物体的中心点。

9. orbit center（轨道中心）：这个单词用来表示一个天体围绕另一个天体运动的中心点。

10. gravity center（重力中心）：这个单词用来表示一个物体的重力场的中心点。

常用短语：

1. circumcenter of mass

2. circumcenter of circle

3. circumradius

4. circumcircle

5. inscribed circle

6. eccentricity

7. farthest point

双语例句：

1. The circumcenter of mass of a triangle is its centroid. (三角形的质心是其重心。)

2. The circumcircle of a triangle is the circle that passes through its vertices and circumcenters. (三角形的外接圆是过其顶点和外心(即质心)的圆。)

3. The eccentricity of a circle is the distance of its center from the circumcenter divided by its radius. (圆的偏心率是其中心到圆心的距离除以半径。)

4. The farthest point from the circumcenter of a triangle is the vertex opposite to the side that is opposite to the farthest point on the opposite side of the base. (三角形外心最远点是底边相对顶点与相对底边相对最远点的顶点。)

英文小作文：

The circumcenter is an important geometric concept that plays a crucial role in determining the properties of a figure. It is the center of a circle that passes through all the points of a figure. In this essay, we will explore the importance of the circumcenter and its applications in various contexts.

Firstly, we can use the circumcenter to find the center of mass or center of gravity of a figure. This is particularly useful in mechanical engineering, where it helps us to understand the balance and stability of structures. By calculating the location of the center of mass, we can determine whether a structure will tip over or collapse under its own weight.

Secondly, the circumcenter plays a crucial role in determining the properties of a triangle. It is the point that is farthest from all three vertices, and it determines the size and shape of the inscribed circle. This property can be used to solve various geometric problems related to triangles, such as finding the length of a side or the angle opposite a vertex.

Finally, the circumcenter is also used in other contexts, such as determining the symmetry and orientation of figures, or in determining the properties of polygons and polylines. By understanding the role of the circumcenter, we can better understand the geometry and topology of figures, and apply it to solve real-world problems.