then the question is,the larger radius D,the small radius d,get the largest number of small circle put in the larger?
[Math] how many smaller circles(radius is equal) I can fit within a larger circle
geometrypacking-problem
Related Solutions
I think what you are looking for is this:
The big circle radius is $r_2=AB$ and the little circle radius $r_1=CB=CE$. Recognizing the right triangle $AEC$ you find the relationship
$$ \sin \frac{\alpha}{2} = \frac{CE}{AC} = \frac{r_1}{r_2-r_1} $$
once you have the angle $\alpha$ you can calculate the number of circles that fit in $2\pi$ as $$N={\rm integer}(\frac{2\pi}{\alpha})$$
The area of a circle is $\pi r^2$, so if you plan to fill up the area of a large circle (radius $R$, area $\pi R^2)$, you'll need $\left( \tfrac Rr \right)^2$ little circles. Just as you found empirically.
Best Answer
The answer can be closely approximated by this equation:
Number of Circles $= 0.83\frac{R_2^2}{r_1^2} - 1.9$ (rounded down to whole number)
where: $R_2$ = radius of larger circle $r_1$ = radius of smaller circle