Jon Perry wrote:
Let C be a 2d container with height h and width w from the non-negative reals. Unit circles (radius 1) can be placed inside the container, and they obey the usual rules of gravity, and do not intersect.
What is the minumum number of unit circles needed to place a circle such that its highest point is of height >= h?
If w<2 then f(h,w)=oo as we cannot place any unit circles into a container of this width.
At w=2, f(h,w)=ceil(h/2)
but for w>2 f becomes much less defined.
Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com
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The usual rules of gravity? I'm not sure what that means. With a "steady" hand, one should be able to always obtain ceil(h/2), albeit metastably.