四种圆周率收敛速度比较 C# 代码

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1万次收敛的圆周率对比。
泰勒级数

沃利斯计算

BBP计算

蒙特卡洛计算

通过对此，被推崇的BBP计算，实质上收敛速度还不如沃利斯计算。
蒙特卡洛估值，带有很大的随意性，误差较大。

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;

namespace PI_Test
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }
//泰勒级数
        private void button1_Click(object sender, EventArgs e)
        {
            double PITest=0;
            for (double i = 1; i < double.Parse(收敛次数.Text); i++)
            {
               PITest=PITest+((1/(2*i-1))*Math.Pow(-1,i-1));             
            }
            结果.Text = (PITest*4).ToString();
        }

        private void Form1_Load(object sender, EventArgs e)
        {
            AcceptButton = button1;
            PI对比.Text = Math.PI.ToString();
        }
//沃利斯
        private void button2_Click(object sender, EventArgs e)
        {
            double PITest = 1;
            for (double i = 1; i < double.Parse(收敛次数.Text); i++)
            {
                PITest = PITest * ((((2 * i) / (2 * i - 1)) *((2 * i) / (2 * i + 1))));
            }

            结果.Text = (PITest*2).ToString();
        }
//BBP计算
        private void button3_Click(object sender, EventArgs e)
        {
            double PItest=0;           
            for (double i = 0; i < double.Parse(收敛次数.Text); i++)
            {
                PItest = PItest + Math.Pow((-1 / 1024),i)
                    *(-32/(4*i+1)-
                    1/(4*i+3)+
                    256/(10*i+1)-
                    64/(10*i+3)-
                    4/(10*i+5)-
                    4/(10*i+7)+
                    1/(10*i+9));
            }
            结果.Text = (PItest/64).ToString();
        }
//蒙特卡洛计算
        private void button4_Click(object sender, EventArgs e)
        {
            double PItest = 0;
            double inside_circle=0;
            double i;
            Random x = new Random();
            int iSeed = x.Next(-10000000, 10000000);
            Random y = new Random(iSeed);

            for (i = 0; i < double.Parse(收敛次数.Text); i++)
            {
                double x1 = x.NextDouble();
                double y1 = y.NextDouble();
                if (x1 * x1 + y1 * y1 < 1)
                {
                    inside_circle = inside_circle + 1;
                }
            }

            PItest = 4*inside_circle / i;
            结果.Text = PItest.ToString();
        }
        private void textBox1_TextChanged(object sender, EventArgs e)
        {

        }
    }
}