Finding the Ratio of Areas in a Circle Arrangement

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The discussion focuses on calculating the ratio of areas in a specific arrangement of circles. One arrangement involves the centers of smaller circles forming a regular octagon, yielding a ratio of approximately 0.28. The conversation clarifies that the ratio of areas can be derived from the ratio of diameters of the circles. There is a suggestion to create a visual representation to confirm the arrangement of the circles. The inquiry emphasizes the importance of understanding the geometric configuration to accurately determine the area ratio.
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How are the circles inside arranged?

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

cookiemonster
 
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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