matlab-pi的近似值代码.doc

利用基于的级数来算的近似数：=164=16程序代码： clear; digits(160); syms x x=sym(0); for k=1:15kx=x+sym(-1)sym(k)-sym(1)/(sym(2)*sym(k)-sym(1)*(sym(16)/sym(5)(sym(2)*sym(k)-sym(1)-sym(4)/sym(239)(sym(2)*sym(k)-sym(1);vpa(x,40)vpa(vpa(pi,60)-x,5)end运算结果：k =1ans =3.183263598326359832635983263598326359833 ans =-0.041671k =2ans =3.14059702932606031430453110657922889815 ans =0.00099562k =3ans =3.141621029325034425046832517116408069706 ans =-0.000028376k =4ans =3.141591772182177295018212291112329795027 ans =8.8141e-7k =5ans =3.14159268240439951724025983607357586049 ans =-2.8815e-8k =6ans =3.141592652615308608149350747666502755367 ans =9.7448e-10k =7ans =3.141592653623554761995504593820311845927 ans =-3.3762e-11k =8ans =3.141592653588602228662171260486978513156 ans =1.191e-12 k =9ans =3.141592653589835847485700672251684395509 ans =-4.2609e-14k =10ans =3.141592653589791696917279619620105448141 ans =1.5415e-15k =11ans =3.141592653589793294747374857715343543379 ans =-5.6285e-17k =12ans =3.141592653589793236391840944671865282509 ans =2.0708e-18k =13ans =3.141592653589793238539324592671865282509 ans =-7.6681e-20k =14ans =3.141592653589793238459788161264457875102 ans =2.8552e-21k =15ans =3.14159265358979323846275020767549235786 ans =-1.0682e-22 从结果看取15项部分和就可以精确到第21位小数。利用高斯公式：=48+3220计算的近似值。程序代码：clear;digits(160);syms xx=sym(0);for k=1:20kx=x+sym(-1)(sym(k)-sym(1)/(sym(2)*sym(k)-sym(1)*(sym(48)/sym(18)(sym(2)*sym(k)-sym(1)+sym(32)/sym(57)(sym(2)*sym(k)-sym(1)-sym(20)/sym(239)(sym(2)*sym(k)-sym(1);vpa(x,40)vpa(vpa(pi,60)-x,5)end运算结果：k =1ans =3.144388167070395654407986493430228290391 ans =-0.0027955 k =2ans =3.141587573607883117581411853379420096518 ans =5.08e-6k =3ans =3.141592664765766446467954462521640720131 ans =-1.1176e-8k =4ans =3.141592653562973161607826508581675751712 ans =2.682e-11k =5ans =3.141592653589860958821758446223180726536 ans =-6.772e-14k =6ans =3.141592653589793061616610170369797078987 ans =1.7685e-16k =7ans =3.141592653589793238935665387734296845639 ans =-4.7302e-19k =8ans =3.141592653589793238461355246142126021642 ans =1.2881e-21k =9ans =3.141592653589793238462646940403496798961 ans =-3.5571e-24k =10ans =3.141592653589793238462643373346576299015 ans =9.9329e-27k =11ans =3.141592653589793238462643383307493623673 ans =-2.7991e-29k =12ans =3.14159265358979323846264338327942340577 ans =7.9478e-32k =13ans =3.141592653589793238462643383279503111327 ans =-2.2713e-34k =14ans =3.141592653589793238462643383279502883545 ans =6.5266e-37k =15ans =3.141592653589793238462643383279502884199 ans =-1.8844e-39 k =16ans =3.141592653589793238462643383279502884197 ans =5.4635e-42k =17ans =3.141592653589793238462643383279502884197 ans =-1.5899e-44k =18ans =3.141592653589793238462643383279502884197 ans =4.6418e-47k =19ans =3.141592653589793238462643383279502884197 ans =-1.3592e-49k =20ans =3.141592653589793238462643383279502884197 ans =3.9903e-52由运算结果可见当取前20项部分和时可以精确到第52位小数。利用拉马努金公式：=计算的近似值。这次我们利用c语言编程来计算。程序代码：#include #include double fun(int n)double s1,s2=1.0,s3=1.0,s4,s;s1=(2*sqrt(2)/9801;int i;for(i=1;i=n;i+)s2=s2*i;int j;for(j=1;j=4*n;j+)s3=s