uva 10451 - Red Huang

有點無聊的公式解

正 n 邊形的面積為

$Deg : A=\frac{nt^2sin(\frac{360}{n})}{4(1-cos(\frac{360}{n}))}$

邊長為_a_ 的正多邊形的內切圓半徑為：

$r_n = \frac{a}{2} \cot(\frac{\pi}{n})$

邊長為_a_的正_n_ 邊形外接圓的半徑為：

$R_n = \frac{a}{2\sin(\frac{\pi}{n})}$

參考自維基百科

//====================================================================||  
//                        Name  : Ancient Village Sports.cpp                             ||  
//                     Date : May 31, 2013 8:09:14 PM                         ||  
//                         Author : GCA                               ||  
//                  6AE7EE02212D47DAD26C32C0FE829006                  ||  
//====================================================================||  
#include <iostream>  
#include <cstdio>  
#include <cstring>  
#include <algorithm>  
#include <cmath>  
#include <climits>  
#include <vector>  
#include <set>  
#include <map>  
#include <queue>  
#include <cctype>  
#include <utility>  
using namespace std;  
#ifdef ONLINE\_JUDGE  
#define ll "%lld"  
#else  
#define ll "%I64d"  
#endif  
typedef unsigned int uint;  
typedef long long int Int;  
#define Set(a,s) memset(a,s,sizeof(a))  
#define Write(w) freopen(w,"w",stdout)  
#define Read(r) freopen(r,"r",stdin)  
#define Pln() printf("\\n")  
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()  
#define De(x)printf(#x"%d\\n",x)  
#define For(i,x)for(int i=0;i<x;i++)  
#define CON(x,y) x##y  
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\  
    printf("%d ",dp\[htx\]\[hty\]);}Pln();}  
#define M 55  
#define PII pair<int,int\>  
#define PB push\_back  
#define oo INT\_MAX  
#define Set\_oo 0x3f  
#define Is\_debug true  
#define debug(...) if(Is\_debug)printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)  
#define FOR(it,c) for(\_\_typeof((c).begin()) it=(c).begin();it!=(c).end();it++)  
#define eps 1e-6  
bool xdy(double x,double y){return x>y+eps;}  
bool xddy(double x,double y){return x>y-eps;}  
bool xcy(double x,double y){return x<y-eps;}  
bool xcdy(double x,double y){return x<y+eps;}  
int min3(int x,int y,int z){  
    int tmp=min(x,y);  
    return min(tmp,z);  
}  
int max3(int x,int y,int z){  
    int tmp=max(x,y);  
    return max(tmp,z);  
}  
double pi=acos(0)\*2;  
double cot(double x){  
    return 1/tan(x);  
}  
int main() {  
    ios\_base::sync\_with\_stdio(0);  
    double a;  
    int n;  
    int ff=0;  
    while(~scanf("%d %lf",&n,&a)&&n>=3){  
        double dn=n\*1.0;  
        double b=sqrt((a\*4\*(1-cos(2\*pi/dn)))/(n\*sin(2\*pi/dn)));  
        double outsider=b/(2\*sin(pi/(n\*1.0)));  
        double outsidea=outsider\*outsider\*pi;  
        double insider=(b/2)\*cot(pi/(n\*1.0));  
        double insidea=insider\*insider\*pi;  
//        debug("%f %f %f %f\\n",outsidea,insidea,a,b);  
        printf("Case %d: %.5f %.5f\\n",++ff,outsidea-a,a-insidea);  
    }  
}