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Suppose I have n ellipses, $\left\lbrace E_i \right\rbrace_{i=1}^n $; each ellipse, $E_i$, has the same area $A_1$. I want to completely cover a region (assume a rectangle) , $R$, with the least (minimize the number of $E_i$'s to cover) amount of $E_i$'s. $R$ has an area of size $A_2$ such that $n \cdot A_1 > A_2$.

EDIT[June 14, 2012] - after further research to what I am looking for, I realize I am looking for a variant of a minimal tiling problem. I have restated the problem here.

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And what is your question? – Harald Hanche-Olsen Jun 9 '12 at 20:49
I changed the tags, since "covering spaces" is an entirely different topic. Is the orientation of ellipses fixed or arbitrary? (BTW, the condition $n\cdot A_1>A_2$ does not guarantee that such a cover exist. You cannot cover a $1\times 1$ square with a single disk of area $1.1$) – user31373 Jun 9 '12 at 20:50

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