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So you want the upper edge of each circle to be exactly on the hemisphere?
See this (sorry for the quick and dirty sketch), where h is the height of all the discs up to that point (including the one you want to find the radius of), and r is the radius of the hemisphere you're looking for.
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SwissChap
moocher
@useless and @danstuff helped out with this before back here
but i'm still struggling.
I want to approximate a hemisphere but I'm just reducing by a fixed amount, whereas I need to reduce by a little bit at first and then gradually more and more.
My parameters are thickness of material, and diameter or radius of the biggest bottom circle.