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April 21st, 2013, 08:02 AM   #1
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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 (:
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April 21st, 2013, 10:57 AM   #2
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Re: 4 circles inside a hexagon

Are the 4 circles the same size?
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April 21st, 2013, 10:58 AM   #3
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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.
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April 21st, 2013, 04:57 PM   #4
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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?
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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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File Type: gif Circles.gif (4.2 KB, 92 views)
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