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Ken's Puzzle of the Week

Circle Around Circles

Place N unit circles (radius=1) together without overlapping. What
is the smallest circle which can be circumscribed around the unit circles?
Solve for N from 1 to 9.

Source: Original (but it exists in many other places.)

Solutions were received only from Kirk Bresniker and Philippe Fondanaiche.
Since there are so many other solution sites already out there, most elected
to just send me "this already exists" notes. Kirk's table is below,
along with several links to solutions.
n d exact d approx.
1 1 1.00000
2 2 2.00000
3 1+2/3sqrt(3) 2.15470...
4 1+sqrt(2) 2.41421...
5 1+sqrt(2(1+1/sqrt(5))) 2.70130...
6 3 3.00000
7 3 3.00000
8 1+csc(pi/7) 3.30476...
9 1+sqrt(2(2+sqrt(2))) 3.61312...

http://www.stetson.edu/~efriedma/cirincir/

http://mathworld.wolfram.com/CirclePacking.html

http://www.packomania.com/

http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html

http://www.buddenbooks.com/jb/pack/circle/index.htm

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