数学实验4答案

第四次练习题

1、 编程找出 5,1000+=≤b c c 的所有勾股数，并问：能否利用通项表示 },,{c b a ? >> for b=1: 995

a=sqrt((b+5)^2-b^2);

if(a==floor(a))

fprintf('a=%i,b=%i,c=%i\n',a,b,b+5)

end

end

a=15,b=20,c=25

a=25,b=60,c=65

a=35,b=120,c=125

a=45,b=200,c=205

a=55,b=300,c=305

a=65,b=420,c=425

a=75,b=560,c=565

a=85,b=720,c=725

a=95,b=900,c=905

>> for c=6:1000

a=sqrt(c^2-(c-5)^2);

if(a==floor(a))

fprintf('a=%i,b=%i,c=%i\n',a,c-5,c)

end

end

a=15,b=20,c=25

a=25,b=60,c=65

a=35,b=120,c=125

a=45,b=200,c=205

a=55,b=300,c=305

a=65,b=420,c=425

a=75,b=560,c=565

a=85,b=720,c=725

a=95,b=900,c=905

{a,b,c}={100*n^2-100*n+25,10*n^2-10*n,10*n^2-10*n+5}

2、编程找出不定方程 )35000(122<-=-y Dy x 的所有正整数解。（学号为单号的取D=2, 学号为双号的取D=5）

D=2（学号为单号）

>> for y=1:34999

x=sqrt(2*y^2-1);

if(x==floor(x))

fprintf('x=%i,y=%i\n',x,y)

end

end

x=1,y=1

x=7,y=5

x=41,y=29

x=239,y=169

x=1393,y=985

x=8119,y=5741

x=47321,y=33461

3、 设 ⎩⎨⎧==+=--1,12121a a ma

a a n n n ， 编程计算.100a （学号为双号的取m=1）

输入：

clear all

clc

an1=1;an2=1;an=0;

for n=3:100

an=an1+an2;

an2=an1;

an1=an;

end

fprintf('N=%i,An=%i\n',n,an); 输出：

N=100,An=3.542248e+020

4、用Monte Carlo 方法计算圆周率π 输入：temp.m

clear all

clc

s=0;

for n=1:100000

r1=rand(1);

r2=rand(1);

if r1^2+r2^2<=1

s=s+1;

end

end

pi=4*s/n;

fprintf('Pi=%E',pi);

输出：

Pi=3.141600E+000

5、实验十练习7：选取10 000对随机的b a ,,根据1),(=b a 的概率求出π的近似值. 输入：temp.m

clear all

clc

s=0;

for n=1:10000.

a=ceil(rand(1)*10000);

b=ceil(rand(1)*10000);

p=a;q=b;

if(p

r=p;p=q;q=r;

end

while q~=0

r=q;q=mod(p,q);p=r;

end

if p==1

s=s+1;

end

end

pi=sqrt(6/(s/10000));

fprintf('Pi=%E',pi);

输出：

Pi=3.146065E+000>>

2007,8.250000,40.875000 2008,8.375000,41.062500 2009,8.312500,40.968750 2010,8.343750,41.015625 2011,8.328125,40.992188 2012,8.335938,41.003906 2013,8.332031,40.998047 2014,8.333984,41.000977 2015,8.333008,40.999512 2016,8.333496,41.000244 2017,8.333252,40.999878 2018,8.333374,41.000061 2019,8.333313,40.999969 2020,8.333344,41.000015 2021,8.333328,40.999992 2022,8.333336,41.000004 2023,8.333332,40.999998 2024,8.333334,41.000001 2025,8.333333,41.000000 2026,8.333333,41.000000 2027,8.333333,41.000000 2028,8.333333,41.000000