The following method of computing was discovered by Archimed

The following method of computing was discovered by Archimedes 1. let A = 1 and N = 6 2. Repeat 10 times, say:

a) Replace N by 2 N

b)  Replace A by [2 -(4-A²)^1/2]^1/2

c) Let L=(N*A)/2

d) U= L / [(1-A²/2)^1/2]

e) Let P = (U+L)/2

f) Let E= (U-L)/2

g) Print N, P, E

3) Stop

Write a program to implement the above algorithm using Matlab

Solution

A=1;

N=6;

for i= 1:10

N=2*N;

A = (2 - (4-2*A)/2)/2;

L= N*A/2;

U= L/((1-A*2/2)/2);

P=(U+L)/2;

E=(U-L)/2;

end

N

P

E