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I Convert 2 variables into 1 representative variable

  1. Nov 9, 2016 #1
    I need help to convert 2 variables A,B into 1 representative variable C, which is used to filter A,B:

    Below is an example with C=A+B, which makes Set 2 the highest value:
    Set 1: A=65, B=75, C=140;
    Set 2: A=50, B=100, C=150;
    Set 3: A=54, B=90, C=144;
    Set 4: A=72, B=72, C=144;
    Set 5: A=71, B=73, C=144;
    Set 6: A=71, B=71, C=142;

    But I want either Set 4 or 5, which has *both* A and B being closer to 100, and also a high A+B value.

    If you know/understand computer code:
    if(C>previousC) isBestSet=SetNumber;

    I do not care if C is a big or small number, meaning I do not care if I need to pick the biggest or smallest C.
  2. jcsd
  3. Nov 9, 2016 #2


    Staff: Mentor

    I'm not sure what adding A and B does for you, but it seems like you want to minimize the distance from a point (A, B) to the point (100, 100)
    For set 4 (the point (72, 72) ), the distance is ##\sqrt{1568}##.
    For set 5 (the point (71, 73) ), the distance is ##\sqrt{1570}##.
    To calculate the distance of a point (A, B) to (100, 100), the formula is ##d = \sqrt{(100 - A)^2 + (100 - B)^2}##.
  4. Nov 9, 2016 #3
    Wow. Perfect. Thank you very much.

    I Googled: "minimize the distance from a point"
    I see that this technique is actually the Pythagorean theorem, which leads me to another question:

    Sometimes my Sets have 3 variables instead of 2.
    Is it safe to *assume* that I simply tack on another: + (100-3rdVar)^2
    (i.e. since there is no real need for me to preform the final square root)

    Thanks again.
  5. Nov 9, 2016 #4


    Staff: Mentor

    Yes, distance in three dimensions is ##d = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2 + (x_3 - y_3)^2}##. And if ##(x_1, x_2, x_3)## and ##(y_1, y_2, y_3)## are the minimum distance apart, the square of their distance, ##d^2##, will also be at a minimum.
  6. Nov 9, 2016 #5


    User Avatar
    2017 Award

    Staff: Mentor

    You can also take the largest difference to 100, C=max(100-A, 100-B). There are many functions, the best for you depends on what exactly you want to prefer over what.

    All methods discussed can be extended to 3 variables easily.
  7. Nov 9, 2016 #6
    Thanks again Mark!

    Thanks anyway, but Mark nailed it for me right on the head.
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