calculate circle cardboard segments

Question

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!

Answer 1

I have interpreted your question as meaning that you want a stack of cardboard circles, making a half sphere when glued together.

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 $\sqrt{\left({y\over2}\right)^2-(nx)^2}$

Correct me if my interpretation is wrong.