Algorithm for Generating Percentage Amounts

[natedgreat3]

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 =]

 

[AlephZero]

The sizes of each wedge form a geometric series.

See http://www.mathsisfun.com/algebra/sequences-sums-geometric.html - or google for geometric series if you don't like that web page.

 

[natedgreat3]

Okay cool, except a geometric series doesn't have to add up to a maximum amount, in this case 100% =/

 

[Office_Shredder]

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.

 

[AlephZero]

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.

 

[natedgreat3]

Thanks guys, you rock =]