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Let's say circle $\omega_1$ has a diameter $X$. Let $X>Y$; $Y\in \mathbf{R}^{+}$. How many circles with diameter $Y$ will fit inside $\omega_1$?

Is there a formula for this?

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You can assume $Y=1$ without loss of generality. –  MJD Aug 16 '13 at 2:08
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Given that many circle packing methods are conjectured (but not proven) optimal, the answer to your question "is there a formula for this" would be no. –  Julien Aug 16 '13 at 13:01
    
you can $\frac{(x-x\%y)}{y}$ with the area. –  user52413 Aug 28 '13 at 8:52

1 Answer 1

$${{\pi {X^2}} \over {\pi {Y^2}}}$$

=$${{{X^2}} \over {{Y^2}}}$$

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This answer would be better if you added some explanation about why computing these quantities is useful. –  yoknapatawpha Aug 28 at 4:25
    
area is a space, when you calculate a circle's area you calculate it's space contained by circumference. how many circles(diameter:-Y) can be drawn within the large circle(diameter:- X) mean the number of area included by the circle( diameter:-Y) into the large circle(diameter:-X)thank you. if you do not satisfy with my answer, please comment blow and say why? –  Kajaan Aug 28 at 15:04
    
This only gives an upper bound for the number of circles of diameter $Y$ which fit into a circle of diameter $X$. However, that upper bound is not attainable (unless $X = Y$). For instance, try packing $4$ circles of diameter $1$ into a larger circle of diameter $2$. You will see that it is not possible. –  JimmyK4542 Oct 6 at 0:44

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