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I researched on this question but could find questions similar to number of circles of radius R1 that could fit in another circle of radius R2. But can we effectively determine, using a standard procedure/algorithm, the minimum circles required to cover a larger circle completely?
PS: I was thinking of some optimal arrangement of the smaller circles in the larger one. And circles can (obviously) overlap.

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    A sort of "inverse problem" or "dual problem" to what you're considering is the [disk covering problem](http://mathworld.wolfram.com/DiskCoveringProblem.html). – 2017-02-07
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    To answer that question, though: there is no "algorithm" currenly known that produces an optimal arrangement. – 2017-02-07
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    Packing problems are usually hard. Depending on R1, R2, the arrangement can be quite irregular. I see no reason for this to be different. – 2017-02-07
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    @Omnomnomnom Is there any specific property if the ratio of radius is `PI`.? – 2017-02-08
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    Base on Wikipedia we know that 13 or more disks are required. That's all I can gather though – 2017-02-08

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This is the dual version of the Disk covering problem. There are some results in this article, and a visualisation for some values of $R_1$ here.

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    Thanx for answering. Can I get to know any specific property if the ratio of radius is `PI`. – 2017-02-08