: 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
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?
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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.
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.
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.
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