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Interesting Problem Again
Posted:
Nov 21, 2002 5:15 PM


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, (lb)
lets us cut off a perfect square out of this rectangle. we will be left with a rectangle of sides (lb), (2b l)
iteration 1 : sides (l,b) iteration 2 : sides (b, lb) iteration 3 : sides (lb, 2bl) ..... .... 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?



