Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
You can assume $Y=1$ without loss of generality. – MJD Aug 16 '13 at 2:08
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. – hasnohat Aug 16 '13 at 13:01
you can $\frac{(x-x\%y)}{y}$ with the area. – user52413 Aug 28 '13 at 8:52

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

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

share|cite|improve this answer
This answer would be better if you added some explanation about why computing these quantities is useful. – yoknapatawpha Aug 28 '14 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 '14 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 '14 at 0:44

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.