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How many circles of 1cm diameter can be packed in a circle of n diameter. I need a formula in terms of n and a valid proof. Do note that the curve in the circle affects the answer.?
Wiki User
∙ 12y ago
There is no simple answer and no single proof. Indeed, for some values of n, the answer is still an unproven conjecture.The smallest radius, r, in which c circles can be packed is as follows:
c = 1: r = 1
c = 2: r = 2
c = 3: r = 1+2/3*sqrt(3) = 2.154...
c = 4: r = 1 + sqrt(2) = 2.414...
c = 5: r = 0.6854...
c = 6: r = 3
c = 7: r = 3
c = 8: r = 1 + 1/sin(pi/7) = 3.304...
c = 9: r = 1 + sqrt[2*(2 + sqrt(2)] = 3.613...
c = 10: r = 3.813...
All these are obvious or proven.
In the next ten, only 11, 12, 13 and 19 have been proven. The conjecture for 20 is 5.122....
Wiki User
∙ 7y ago
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