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February 10th, 2012, 08:27 AM   #1
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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

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February 10th, 2012, 05:06 PM   #2
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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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