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Math Help - Shrink numbers within a range preserving distance ratio

  1. #1
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    Shrink numbers within a range preserving distance ratio

    I am not sure whether this problem would belong to Algebra or set Theory, hopefully it belongs here... I am not a mathematician, so its hard for me to come to a concrete category. I am trying to solve a problem at hand, and I need to get this necessary step done in order to find a complete solution.


    Problem Description:
    Suppose I have some points spread (unequally) on a line within some range. I want to shrink the points within a smaller range, so that the old distance ratio between points remain preserved.

    e.g.

    I have points a,b,c,d,e,f,g spread between Range X & Y

    X = 0.25 Y = 0.90
    a = 0.25 , b=0.32 , c=0.45, , d=0.50, e=0.60, f=0.80, , g=0.90

    As we can see above that the distances are uneuqal between the spreaded points. Now, I want to shrink these points to a smaller range X' & Y',

    where
    X' = 0.35 Y' = 0.65

    How would I calculate values of a',b',c',d',e',f',g' , such that the distance ration between all these points remain same for the smaller range.

    a' = ? , b'=? , c'=?, , d'=?, e'=?, f'=?, , g'=?

    I have been trying to come up with a formula that would help me solve this problem, but am unable to formulate one.

    I hope someone here can help me.
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  2. #2
    Junior Member
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    A simple way to do that is to regard the points as fractions of your original interval.

    Call L=Y-X and the 'ratio to the interval' F_i = \frac{a_i-X}{L} your new coordinates will then be a_i' = X' + F_iL'
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  3. #3
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    Quote Originally Posted by brouwer View Post
    A simple way to do that is to regard the points as fractions of your original interval.

    Call L=Y-X and the 'ratio to the interval' F_i = \frac{a_i-X}{L} your new coordinates will then be a_i' = X' + F_iL'
    Thanks alot... I think this solution would work perfectly for me...
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