fzu 1330:Center of Gravity（计算几何，求扇形重心）

Problem 1330 Center of Gravity

Accept: 443    Submit: 830
Time Limit: 1000 mSec    Memory Limit : 32768 KB

 Problem Description

Given a sector of radius R, central angle P. You are to calculate the distance between the center of gravity and the center of the circle.

 Input

Given a sector of radius R, central angle P. You are to calculate the distance between the center of gravity and the center of the circle.

 Output

Given a sector of radius R, central angle P. You are to calculate the distance between the center of gravity and the center of the circle.

 Sample Input

0.01 6.28

 Sample Output

0.000003

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　　计算几何，求扇形的重心。

　　看的教程里有求扇形重心的公式，我就直接拿来用了：

　　

　　

　　可以看出，这里求的重心位置是重心到圆心的距离，正好是这道题求得值。

　　代码：

 1 #include <stdio.h>
 2 #include <math.h>
 3 int main()  4 {  5     double r,p;  6     while(scanf("%lf%lf",&r,&p)!=EOF){  7         double z;    //扇形重心
 8         p/=2;  9         // 求扇形重心公式一 10         //double b = r*sin(p); //圆心角对应的弦长 11         //double s = p*r; //圆心角对应的弧长 12         //z = 2*r*b/(3*s); 13         //公式二
14         z = 2*r*sin(p)/(3*p); 15         printf("%lf\n",z); 16  } 17     return 0; 18 }

 　　PS：公式一是公式二的推导后的公式。

 

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