# calculate circle cardboard segments

I want to make a cardboard lamp, but i want it to look like half a sphere.

Given a cardboard thickness of x, and a circle width of y, how many elements do I need and what radius do the elements need to be? Anyone got a formula for that?

thanks alot!

• by half a circle, do you mean half a sphere? could you be more clear? my interpretation is that you want to stack up many cardboard circles to make a half of a sphere. Is this right? – stanley dodds Apr 30 '16 at 14:34
• so does my answer use the correct interpretation? It looks like it does from the image you have given - thanks for that, also. – stanley dodds Apr 30 '16 at 14:52
• yes, i meant half a sphere! (not native english) – pvc May 4 '16 at 18:11

If this is the case, then you will need $y\over2x$ individual cardboard rings.
Starting from the bottom, if you are on the $n^{th}$ ring up (the first ring at the bottom is $n=0$) then the formula for the ring's radius is $\sqrt{\left({y\over2}\right)^2-(nx)^2}$