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April 21st, 2013, 08:02 AM  #1 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  4 circles inside a hexagon
I have a task for school and I have to find the most efficient way to fit 4 circles inside a hexagon. By efficient I mean that the hexagon is as small as possible. I tried to place my circles in a square, but it looked like if I put it in a rhombus my hexagon would be smaller, but then I don't know how to get the measurements of that rhombus /: so could anyone help me with this? Thanks in advance if anyone has a question because I'm not clear enough, feel free to ask it (: 
April 21st, 2013, 10:57 AM  #2 
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  Re: 4 circles inside a hexagon
Are the 4 circles the same size?

April 21st, 2013, 10:58 AM  #3 
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  Re: 4 circles inside a hexagon
Hello gelatine1, I've got a circle packing problem I'm too lazy to solve. http://www.flickr.com/photos/85937466@N ... 841474850/ See if can solve that one. Think of it like a video game. The first stage is the easy stage. Then the next stage is harder. By the way my solution on that page is incorrect. 
April 21st, 2013, 04:57 PM  #4 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: 4 circles inside a hexagon
Yeah, the circles have all a radius of 3. Oh and I forgot to mention that the hexagon should be regular. But I have tried to put them in a square again but I turned my hexagon a bit and now it looks like this is the best way to do it. Can anyone confirm that? 
April 27th, 2013, 09:13 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,641 Thanks: 2083 
[attachment=0:3ipqzc7z]Circles.gif[/attachment:3ipqzc7z] The circles above are not quite in a square configuration, but I suspect the configuration is optimal. If necessary, click once on the diagram to avoid having to scroll. I didn't calculate the exact size of the hexagon, but as it's very close to 8, it may be exactly 8. 

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