circle-packing question: How many 1.328-diameter circles can

S

sav99

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Feb 26, 2007
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Can anyone tell me the formula I need to find out the following?

How many 1.328 diameter circles can I fit in a 18 inch diameter circle? (All of the 1.328 inch circles need to be tangent to each other.)

Thank you!

Glen
 
I think the discovery is the interesting part of the problem. Draw your space and start cramming them in. See what you get in various configurations.

Personally, I would first calculate a ridiculouly large value, just to make sure I don't get too far off. In this case, the super-upper bound might be if you smashed circles to take up all the space with none wasted. You can't do that with real circles, so this will give some guidance about the limit.

(Area of Space)/(Area of 1 Circle) = (Super-Upper Bound)
 
I found the area of the big circle . I found the area of the small circle . I divided the larger area by the smaller area and computed an answer of 183 ........ this is not correct . I used solid modeling software to compare that answer , and I get an answer of 151 .......

bobring.jpg
 
so ....... is there a formula I can use rather than using this software ? ......
 
sav99 said:
computed an answer of 183 ........ this is not correct
Click to expand...
It is exactly correct for what it was intended to be, a gross overestimate. If you can find a way to stuff in 200, then you did something wrong. As you can see, the software gave a value somewhat less than that. This is exactly as expected.
 
So ...... is there anyway to get an answer that isn't " grossly over-estimated " ? ............. we didn't get to the moon by grossly over-estimating ......

I'm just looking for an equation that is accurate . If you don't have one , that is fine .... thanks for responding .
 
I answered that in the first post. Since we don't know who you are, and you haven't told us, and we would have no way to verrify what you told us, I'm still waiting for you to show some effort. It isn't our business to do anyone's homework for them or to win any contests for anyone.

personally, I'd line up a diameter and see what I could wedge in after that.
 
I posted a jpeg of a solid model that I rendered on software costing 8K a station , and you think this is homework ???
 
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