数学计算-圆周率计算算法

圆周率计算算法

计算方法 一：圆等分法

主要思想是把圆等分，求多边形的周长，分的份数越多，多边形的周长则越接近圆的周长。

Y(n)^2 = 2-sqrt(4-Y(n-1)^2)

PI = 3*(2^n)*Y(n)

#include <>
#include <>
#include <>

// start from 6 edges
double PI_calc(int n)
{
    int nEdge = 6;
    int i = 0;
    double len = 1;
    double PI = 0;
    int k = 3;

    while(i <= n)
    {
        PI = k * sqrt(len);
        printf("edges=%d k=%d, len=%10f,  PI=%36f\n", nEdge, k, len, PI);

        nEdge *= 2;
        len = 2 - sqrt(4 - len);
        k = k * 2;

        i++;
    }

    return PI;
}

int main()
{
    int ch;
    double PI = PI_calc(18);

    scanf("%c", ch);
    return 0;
}

计算方法 二：级数法

PI = 2 * (1 + 1/3 + (1/3) * (2/5) + (1/3) * (2/5) * (3/7) + (1/3) * (2/5) * (3/7)*(4/9) + ........)

#include <>

double PI_calc(int n)
{
    int i = 0;
    double  k = 0;
    double  y  = 1.0;
    double  PI = 0;
    double  m = 1.0;

    while (i <= n)
    {
        PI = 2 * y;
        printf("i=%d, y=%f   PI=%f\n", i, y, PI);
        i++;
        k++;
        m = m * (k/(2*k+1));
        y = m + y;
    }

   return PI;
}

int main()
{
    char ch;

    PI_calc(50);
    scanf("%c", ch);

    return 0;
}