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Topic: Interesting Problem Again
Replies: 1   Last Post: Nov 21, 2002 8:38 PM

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Posts: 6
Registered: 12/13/04
Interesting Problem Again
Posted: Nov 21, 2002 5:15 PM
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Hi I did post a message before but it is not appearing properly.

I am repeating the problem here.

Let us take a rectangle having sides l, b

l > b

let us cut off a perfect square out of this rectangle. so the
remaining will be a rectangle of sides b, (l-b)

lets us cut off a perfect square out of this rectangle. we will be
left with a rectangle of sides (l-b), (2b -l)

iteration 1 : sides (l,b)
iteration 2 : sides (b, l-b)
iteration 3 : sides (l-b, 2b-l)
iteration n : sides (function(l,b,n)???, function(l,b,n)

At what point the left out rectangle becomes a square and no more
iterations is possible?

iteration end : sides (a,a) [a = ?] and iteration number of end = ?

Is there a series for this problem? Anyone tried to solve this?
This seems to be interesting to me...
Since the process we do looks repetitive to the rectangle,
there may be a way to solve these two problems
as functions of the sides of the given triangle...

Any takers?

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