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Thuged_Out_G

Mon Oct 27, 2003 10:39 pm


Babylonian method of Square roots

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the babylonia method for calculating square roots involves iteration. Suppose you wish to find the square root of 5. The babylonian method starts with a wild card guess which we will call x. You then use the iteration rule where the next x equals 0.5(x+n/x). For example, if we start with x=10, then the next x would be 0.5(10+5/10) or 5.25. We use that new value for x to determine the next value. This continues until x converges on a specific value. As the difference in x values becomes very small you now have an approximation for the square root of 5. The formula for any positive square root n is x0.5(x+n/x). Write a function that approximates the square root of a number using the babylonian method. You should stop iterations when the value doesnt change to 2 decimal places.

i have to have this function done for comp sci class....can anyone help?
thanks


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Tony

Mon Oct 27, 2003 10:53 pm



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well function is already writen for you there, you just need to put that in a continues loop :roll: 


var x:real
var x2:real
var n:real

put "what number to square root?"
get n

x:=n

loop
x2:=x*0.5*(x+n/x)
x:=x2
put x2
end loop


although I dont quite understand how this is suppost to find anything :? It skips 5.

just use

put 25**(1/2)

 :lol:


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Thuged_Out_G

Mon Oct 27, 2003 10:54 pm



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lol

i would, but i have to hand this is...its the final proggy for the functions unit lol


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Dan

Mon Oct 27, 2003 10:57 pm



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well if x is a guess you whould probly whont to set it to a number graeter then the one you are finding  the square root for. so set x to somting like: num to find  square  root of + 1. then just do thous math staments in your post in a loop that stops when the number is the the rigth range. you will most likey need to use real variables for this beacuse you need the demalses.

EDIT: dang tony and his fast posting


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Tony

Mon Oct 27, 2003 10:59 pm



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well the function seems to be messed up...

actually you can try to trim the value to keep on going

like

put strreal(realstr(1.23456789011111111,0))



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Thuged_Out_G

Mon Oct 27, 2003 11:01 pm



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var winID:int
winID:=Window.Open("position:top,center,graphics:640;640")

function babylon(n:real):real
    var i,x,x1,x2,x3:real
    loop
    i:=Rand.Int(5,10)
    x:=0.5*(i + n/ i)
    x1:=0.5*(x + n / x)
    x2:=0.5*(x1 + n / x1)
    x3:=0.5*(x2 + n / x2)
    result x3
    end loop
end babylon

var n:real


for  root:1..1000000
put "Enter in the number(0 to exit): "..
get n
put babylon(n)
if n=0 then
loop
Window.Close(winID)
end loop
end if
end for


thats what i have so far, and it works....but it just gets less accurate the higher the number you put...it seems towork for values up to 10,000[/code]


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Tony

Mon Oct 27, 2003 11:08 pm



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that's because for values of 10,000, you need to calculate new value more then 3 times (meaning have x4).

and why is there a loop in function? It NEVER gets to endloop because of result