Finding the Ratio of Areas in a Circle Arrangement

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In summary, the conversation is discussing the arrangement of circles inside a larger circle. The ratio of the areas of the small circles to the large circle is about 0.28 and involves the centers of the small circles forming a regular octagon. The speaker suggests using a simple image to show the arrangement of the circles and questions if it is possible for 8 circles to be arranged in this way.
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Itachi
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  • #2
How are the circles inside arranged?

cookiemonster
 
  • #3
For one particular arrangement, the answer will be about 0.28. This involves the centers of the little circles forming a regular octagon.
 
  • #4
Actually this is sin(Pi/8) / [ 1 + sin(Pi/8) ]
 
  • #5
And which ratio are you looking for? The ratio of the areas or the ratio of the radii or diameters?

cookiemonster
 
  • #6
Itachi said:
the area of one small circle to the large circle
I think, if you know that:

...its like one small circle and 7 small circles around that. The large circle will have a diameter of 3 smaller circles...

then you should be able to find the answer easily. If you have the ratio of diameters, surely you can find the ratio of the areas. However, are you sure this is true? Can 8 circles be arranged in such a way? Perhaps you can make a simple .bmp image and attach it to show how exactly the circles should be touching.
 

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