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Square root operation and scales

  1. Jul 20, 2009 #1
    this is a strange problem easy to solve but I am having trouble understanding it intuitivly.

    Assume we choose a location point and name it 0. Next, in arbitrary direction and distance we place the number 1. Hence, we have created a scale(number line) that extends as much as we like. Now we consider the square root operation(no need to state it). Suppose I choose a number thats hasn't a whole root... for instance lets choose 8.

    Now consider this carefully: We take our scale and we stretch(by a factor of 8) so that the orgin remains unchanged but now what used to be 1 is 8 and what used to be 8 is now 64. Now if we take the square root of 64 we get 8. But heres the problem, we mark the place where 8 was the square root and we squeeze the scale back down to its original size only now the place we marked as 8 which was the square root is not at 1 but rather about 2.828

    ( I figured out that square root of 64 is 8 and square root of 8 when rounded gives 2.828)
    But this problem is showing something about the square root operation on different scales(on a scale transformation). If someone could help to understand the intuition here I would greatly appreciate.
     
  2. jcsd
  3. Jul 21, 2009 #2
    Your stretching transformation is linear, but the sqrt function isn't (just look at the graph y = sqrt x)

    I think I understand what you're asking, but I'm rubbish with words >.<
     
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