Circle with inner rings of equal area?

I'd like to create a circle with rings of equal area (as opposed to rings of equal thickness). The inner ring ends up being a filled circle, and there are two extra rings, for a total of three(3).Here is what I have, which doesn't satisfy the constraint, but just to give an idea:

I `selected`, `filled`, `shrink`, `filled`, `shrink` and `filled` (BGR). I could try taking into account the math beforehand, but I'm wondering if there is a simple way to do this, either with Gimp or other software used in graphic design?

• If you want the actual area then you're going to need to use math.
– Ryan
Commented Nov 13, 2014 at 3:23
• Yes, you can draw circles with The Gimp. But you'll have to ask this on Mathematics.se to get help with the math part.
– DA01
Commented Nov 13, 2014 at 3:55
• Thank you both, I included the link to the math Q in my OP for context; but the angle was I don't know software like Illustrator and people often talk about substracting shapes etc... I thought maybe something along those lines was possible. I know this can be programmed...
– user29318
Commented Nov 13, 2014 at 8:13
• this really depends on your definition of simple. In my mind easiest way is to script it, but you can use the square root spiral. Or just use mathematica. Commented Nov 13, 2014 at 15:29
• Perhaps is simpler to you use Inkscape to draw, resize (using the diameters calculated following the answer of JoKnowBody) and align the circles. Commented Nov 13, 2014 at 17:49

3 Answers

If you start with the disc in the middle, you know its radius in pixels: `R_red`. The area `A` of the disc is

`A=pi*R_red**2`.

`A` is also the area of the green and blue area, respectively. Therefore, the outer radius of the green ring belongs to a disc with area `2*A`.

`R_green = sqrt(2*A/pi))`, and consequently

`R_blue=sqrt(3*A/pi))`.

So, `R_green` is `sqrt(2)` times bigger than `R_red`, and `R_blue` is `sqrt(3)` times bigger than `R_red`.

• Thank you! Yes that is the method employed and that's how I approached trying to make this with Processing. Then I realized starting from the center going outward doesn't make it very predictable in terms of layout/design; someone provided me with a version that starts with a fixed circle size and draws inward. See here.
– user29318
Commented Dec 13, 2014 at 2:33
• Of course, if you specify the number of rings and the outer radius you can reorder the formula. Commented Dec 15, 2014 at 7:07
• Thank you, yes indeed. I consider "calculating it" is a valid answer to my Q; I'll deduce that GD core software doesn't offer such facilities. Thanks again!
– user29318
Commented Dec 16, 2014 at 21:26

Some one did ask a similar question on Mathematics SE -> How to divide a circle into 9 rings / 1 inner circle with the same area?

You will have to adjust the equation a bit.

• Thank you! Please note I had included this very link in my Q.
– user29318
Commented Nov 13, 2014 at 8:13
• Really great question, got my gears turning. You welcome, sorry I can't help with GIMP (I've never used it). I had the same thought DA01 had, so I figure I see if there as already an answer. Commented Nov 13, 2014 at 16:24
• If you're into that sort of things you'll enjoy these implementations. I also failed 10px short of doing it right in this case in some sister language herelol. But I was looking to learn something about how to approach the problem using the GD software...
– user29318
Commented Nov 13, 2014 at 23:27

in adobe illustrator : draw the circle in any size you want , then copy it. after that past in the same place and use the selection tool (v) to re-size it with keep clicking on alt with shift buttons. copy the new one and past it in the place and then click on Ctrl+D 2 times.

• Thank you, but this would be arbitrary. There is a mathematical relationship between the rings and it must be expressed. With prior calculations, of course you would know exactly the radius of each circle so you could scale down accordingly. I was looking for assistance and feedback in that respect from the software...
– user29318
Commented Nov 13, 2014 at 23:30