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Algorithm for Generating Percentage Amounts

  1. Jan 28, 2014 #1
    Hey guys,

    Not totally sure this thread belongs in this section, feel free to move.

    I'm trying to formulate an algorithm for an unusual problem.

    - Generate a pie chart with X number of wedges.
    - Each wedge is X percentage bigger then the one before it.
    - Percentage amounts of all wedges must add up to 100 (thereby completing the pie chart)

    So for example, in Excel I can create a pie chart with 5 wedges, and each wedge is 20% bigger then the previous one. It gives me these numbers (rounded).

    Wedge 1: 13.43797%
    Wedge 2: 16.125564%
    Wedge 3: 19.3506768%
    Wedge 4: 23.22081216%
    Wedge 5: 27.86497459%

    But I got that result by trial and error of Wedge 1's value until the final output of the pie chart hit 100%. How do I calculate Wedge 1's value simply based off the number of wedges in the pie, and the percentage amounts from one wedge to the next?

    I appreciate any help you guys can provide =]
  2. jcsd
  3. Jan 29, 2014 #2


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  4. Jan 29, 2014 #3
    Okay cool, except a geometric series doesn't have to add up to a maximum amount, in this case 100% =/
  5. Jan 29, 2014 #4


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    That's where doing math comes in. If your starting wedge has a%, then you want
    a + 1.2a + (1.2)2a + 1.23a + 1.24a = 100

    Notice that 1.2 a is 20% larger than a, and 1.22a is 20% larger than 1.2a, etc. Now all you have to do is solve for a.
  6. Jan 29, 2014 #5


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    If you don't like algebra, suppose the first wedge is size 1.
    You then have 5 wedges with sizes 1, 1.2, 1.44, 1.728, 2.0736 which add up to 7.4416
    So you need to scale up the sizes by 100 / 7.4416 = 13.43797 - which is what you got by trial and error.
  7. Jan 29, 2014 #6
    Thanks guys, you rock =]
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