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ranjitr303
Member since Nov2310

Nov2310, 10:01 AM (EST) 

"circle in circle"

how many circles of radius r can fit in a bigger circle of radius R ? ans: let n denote the maximum number of circles that can fit in the bigger circle n = 180/(sin^1)(4*(r^2)/(R^2)) (approximately) where sin^1 denotes sine inverse r^2 denote r squared R^2 denote R squared IS THE FORMULA CORRECT ? IF NO PLEASE SEND THE CORRECT ANSWER ?
ranjitr 

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alexb
Charter Member
2668 posts 
Nov2310, 10:06 AM (EST) 

1. "RE: circle in circle"
In response to message #0

>IS THE FORMULA CORRECT ? Honestly? I've no idea. I do not understand what does "approximately" mean. For R = 3r, there seems to be a rather noticeable discrepancy. 

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jmolokach
Member since Aug1710

Nov2310, 12:13 PM (EST) 

2. "RE: circle in circle"
In response to message #0

I got n = 180 / , but this would only work for convenient values of (r,R) where the ratios of r:R are likely not integers. I have a feeling that my formula must be embedded into some greatest integer function? Or perhaps a GIF somewhere embedded in the formula...not sure Here is a table of values for r, R, n using the formula I have and r = 1 ... r R n 1 2 2 1 3 6 1 4 9.244412735 1 5 12.43307536 1 6 15.60203165 1 7 18.76159266 1 8 21.91591164 1 9 25.06699928 1 10 28.21595144 I would love to see someone write an applet for this sort of thing...
molokach 

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jmolokach
Member since Aug1710

Nov2310, 12:33 PM (EST) 

4. "RE: circle in circle"
In response to message #2

OK let me try this again since it didn't post correctly.. n = 180 / arcsin (r/(R  r)) That was my original intent and it apparently got left out of the message somehow... molokach 

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jmolokach
Member since Aug1710

Nov2810, 08:54 AM (EST) 

7. "RE: circle in circle"
In response to message #4

Never mind. The formula I gave appears to be incorrect as I conjecture that if R = 5 you can only fit 12 units circles... and according the to wikipedia page I referenced, you should be able to fit 19. I would be interested in the correct formula. There is yet another table here: https://mathworld.wolfram.com/CirclePacking.html ...but again no formula is given. Although the nested radicals make me think trig identity somewhere... Good luck! molokach 

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jmolokach
Member since Aug1710

Nov2310, 12:13 PM (EST) 

3. "RE: circle in circle"
In response to message #0

It'should also be noted that R must be greater than or equal to 2r in order for the formula to work... any r < R < 2r would give the answer "1" for n I suppose.... So maybe even perhaps the formula should be given piecewise? molokach 

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