My Math Forum Circles inside a circle

 Algebra Pre-Algebra and Basic Algebra Math Forum

 February 10th, 2012, 08:27 AM #1 Senior Member   Joined: Jan 2011 Posts: 560 Thanks: 1 Circles inside a circle Let k circles be c(1),c(2),c(3),....c(k) Let d(i) be the diameter of c(i) with d(1)=r d(i+1)=d(i)+r r is an integer > 0 Can you find the MINIMAL diameter OF ANOTHER circle where you can place all the circles c(i) with i=1 to k. Keep in mind that no intersection is allowed between the circles c(i) I do not think that the computer will be helpful in such. I maybe wrong. Picture to illustrate the case
 February 10th, 2012, 05:06 PM #2 Senior Member   Joined: Jan 2011 Posts: 560 Thanks: 1 Re: Circles inside a circle Let me give you an example. You have 20 circles c(i) i=1 to 20. The diameter of c(1) is 1 cm d(1)=1cm d(2)=2 cms d(3)=3 cms ..... d(19)= 19 cms d(20)=20 cms What is the minimal diameter of the circle where you can place all the 20 circles? No intersection is allowed. Circles can touch each one another. So circles can share at most one point. Good luck! If you find a general formula then the Fields medal is on the sight

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