How many circles can fit inside a circle?

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The discussion focuses on determining how many smaller circles with radius r can fit inside a larger circle with radius R. The formula provided for calculating the number of smaller circles is n = [π/sin^(-1)(r/R)], where [ ] denotes the floor function. Participants express a desire for a proof of this equation, highlighting a lack of resources to verify it. The conversation reflects a mix of curiosity and humor regarding the difficulty of finding a proof. Overall, the thread emphasizes the mathematical exploration of circle packing within a larger circle.
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A circle with the radius R cuts the centers of circles with the radius r that does mearly touch each other, What is the equation for the number of circles in the circle?
 
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No.~of~circles,~n=[\frac{\pi}{sin^{-1}(r/R)}]

where [ ] represents the greatest integer (or floor) function.
 
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Can you give a proof please?
 
You cant? :smile: And I am too lazy to look it up at the library...
 
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