My Math Forum 4 circles inside a hexagon

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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
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[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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