Does the area Apollonian Gasket go to zero?

Asked Nov 27 '24 at 06:18

Active Nov 27 '24 at 11:58

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Does the total area of circles of Apollonian Gasket approach the area of the main circle?

Edit Original question was: Covering circle with circles The unit square can be trivially be covered by squares of geometric progression like $$3\sum_{k=1} \frac{1}{4^k}$$ Is there any covering of a circle by circles that are fully contained in the main circle? but a better phrasing of the question should use Apollonian Gasket, thanks to comment by @CosmicOscillator

edited Nov 27 '24 at 11:58

asked Nov 27 '24 at 06:18

jimjim

9,855

I feel like circle packing problems would be a lot less interesting if there were (if overlap is not allowed; the problem is trivial if it is). – PrincessEev Nov 27 '24 at 06:25
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Maybe you're thinking of something like the Apollonian Gasket? – masky Nov 27 '24 at 07:11
@CosmicOscillator : does the area of circles approach the area of the main circle? – jimjim Nov 27 '24 at 08:19
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@jimjim Yes, the area does seem to approach that of the main circle. See here. – masky Nov 27 '24 at 19:35
@CosmicOscillator thank you , wish that was answer so that I could accept it – jimjim Nov 27 '24 at 22:38

Does the area Apollonian Gasket go to zero?

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