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Q: Formula: How many small circles will fit inside one larger circle? ( No Answer,   0 Comments )
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 Subject: Formula: How many small circles will fit inside one larger circle? Category: Science > Math Asked by: capri712-ga List Price: \$15.00 Posted: 26 Nov 2005 04:22 PST Expires: 26 Dec 2005 04:22 PST Question ID: 597709
 ```How smaller circles will fit inside one big circle? My question is realted to construction in the cellular phone tower industry. I would like a formula or equation to determine how many 6" Circles (Conduits) will fit inside one larger 26" circle (Monopole)? I would like to be able to figure this out in the future with different dimensions (inches).``` Request for Question Clarification by pafalafa-ga on 26 Nov 2005 06:54 PST ```Apparently, there's no straightforward formula for this tricker-than-you'd-expect math problem. There are some sites you can visit which provide answers for a range of diameters, however. Try this one: http://www.stetson.edu/~efriedma/cirincir/ Circles in Circles For the case you mentioned, 6" conduits inside a 26" pipe, the ratio of the diameters is: 26/6 = 4.333 which should allow you to get 14 conduits in the pipe. This is because the value shown for 14 circles is r = 4.328 (smaller than 4.333), while the next value up -- at 4.521 -- is a bit too large. I'm assuming, of course, that the 26" is the *inside* dimension of the pipe. The above link should give you some good rules of thumb for at least 20 conduits in a pipe, with the smaller diameter being about one-fifth the size of the larger pipe. Larger ratios than 1:5, however, and you're on your own! Does that help? pafalafa-ga``` Request for Question Clarification by pafalafa-ga on 26 Nov 2005 07:54 PST ```Here's another table that will cover you up to hundreds of circles-in-a-circle: http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html It's intended for mathmeticians and programmers, but the use of the table is the same as above. Find your ratio, and then look up the ratio in the table that's just smaller than the one you're dealing with. The number in the N column, on the left hand side, is the number of circles that will fit... a ratio of 4.333, again, gives an answer of 14 circles. paf```