
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 

Tags 
circle, circles, inside 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
circle inscribed inside parabolic sector  galactus  Calculus  5  September 3rd, 2015 01:45 PM 
Minimum diameter of a circle to fit other circles inside  Ash  Algebra  1  March 12th, 2014 09:50 AM 
4 circles inside a hexagon  gelatine1  Algebra  4  April 27th, 2013 09:13 AM 
Ellipse inside a circle  intersection  Andromedus  Algebra  18  February 3rd, 2012 12:03 PM 
Circle inside Circle (ask)  sir anrava  Algebra  1  January 19th, 2010 11:18 AM 