Π的计算

首先给出10位精度的?的值3.141592653，用于比较实验得出值 n=1000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]]; N[4*m/n,10]] 运行结果为3.232000000 误差0.090407343

其中n是我们实验的次数。接下来我们增加实验的次数 n=2000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]]; N[4*m/n,10]] 结果为3.168000000 误差 0.026407347 n=3000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]]; N[4*m/n,10]] 结果为 3.152000000 误差 0.010407347

n=4000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]]; N[4*m/n,10]] 结果为 3.145000000 误差0.003407347 n=5000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]]; N[4*m/n,10]] 结果为 3.159200000 误差 0.0176073470 n=6000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]]; N[4*m/n,10]] 结果为 3.151333333 误差 0.00974068

n=7000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]]; N[4*m/n,10]] 结果为 3.169714286 误差 0.028121633 n=8000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]];

N[4*m/n,10]] 结果为3.147500000 误差0.005907347 n=9000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]];

N[4*m/n,10]] 结果为 3.145333333 误差 0.00304768

n=10000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]];

N[4*m/n,10]] 结果为 3.140000000 误差0.001592653 n=20000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]]; N[4*m/n,10]] 结果为 3.119200000 误差 0.022392653 n=30000;

jieguo=Block[{i,m=0},For[i=n,i>0,i--,m=m+If[Random[]^2+Random[]^2?1,1,0]]; N[4*m/n,10]] 结果为 3.152000000 误差 0.010407347 n=60000;