Question

can someone help me undersntad this example in yahoo:

Answer 1

http://answers.yahoo.com/question/index?qid=20090822171107AAPqXzQ

Answer 2

how did they choose 5 and 2?

Answer 3

i am talking about the top answer on there

Answer 4

using bahaskar-bouckner algorithem

Answer 5

5/2 is an approximation of sqrt(5)

Answer 6

so for this method we have to use 5/2 as a starting point

Answer 7

no.

Answer 8

well i mean in this case cause n=5 right?

Answer 9

but if i wanted to find square root of 45, using the bhaskara method i would start with 45/2

Answer 10

no try it with 6/2 :)

Answer 11

your smart guy ehh:)

Answer 12

just takes longer to get closer to the value if you start from farther away

Answer 13

okay i got it broski, was just not sure about how to start it, cause am writing a program for it, but i like to actually work out the first few terms on paper, so i know what i am doing

Answer 14

sqrt(45) is 3sqrt(5) so you'd probably start with 3*5/2

Answer 15

I don't think it matters, I don't think you can diverge from the value if you pick a wild starting approximation... it just takes more steps to get a useful approximation..

Answer 16

cool

Answer 17

theres an old method I'm which you split the number in pairs working from right as follows

Answer 18

Brounker:=proc(n,m)
local a,b,i;
a[1]:=1;
b[1]:=1;


for i from 1 to m-1 do
a[i+1]:=a[i]+b[i]*n;
b[i+1]:=a[i]+b[i];

end do;
return a[m]/b[m],evalf(abs(a[m]/b[m]-sqrt(n)));
end proc;

Answer 19

Basically this is the directions:
For a positive integer n, an iteration is known as the Bhaskara-Brouncker algorithm for approximating √ n by rational numbers ai/ bi , where ai, and bi for i = 1, 2, . . . are integers defined by the recurrence formula ai+1 = ai + bi · n, bi+1 = ai + bi for i = 1, 2, . . . where a1 = b1 = 1. Write a program that, for input positive integers n and m, carries out the iteration for m steps and outputs am /bm and the error am bm − √ n