# 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 Nov 13 '14 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 Nov 13 '14 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 Nov 13 '14 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. – joojaa Nov 13 '14 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. – Paolo Gibellini Nov 13 '14 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 Dec 13 '14 at 2:33
• Of course, if you specify the number of rings and the outer radius you can reorder the formula. – Aziraphale Dec 15 '14 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 Dec 16 '14 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 Nov 13 '14 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. – Kukka Nov 13 '14 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 Nov 13 '14 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 Nov 13 '14 at 23:30