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Sorry, if this question is dumb, but:

When you try to fill the circle with other circles - its called Apollonian circles, and there are resources about it, and some example algorithms. But i want to know the name of the generic algorithm of placing circles within the polygon, in same fashion as apollonian ones are placed in the circle.

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    thanx for a downvote, my anonymous friend ! _though, hopefully, there are some less hostile math geeks here, who can answer my question_2012-01-23
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    I think I would call it an Apollonian packing of the polygon. I don't know if there's a standard name for it.2012-01-24
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    Ha! **[Packing](http://en.wikipedia.org/wiki/Circle_packing)** - its indeed called like that. Thanx, and if you can put your comment as answer, i will accept it (as now i can google my way through it).2012-01-24
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    Your wish is my command.2012-01-24

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It appears that it is called an Apollonian packing of the polygon.