MathOverflow is a question and answer site for professional mathematicians. 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

If I have a square and want to place four equally large circles within this square, how large can the maximum radius be (compared to the lenght of the side of the square)?

Just an answer would be ok, but answer and explanation would be better.

share|cite|improve this question
This sort of question works better on the sites mentioned in the FAQ. – Loop Space May 9 '10 at 20:23
I agree with Andrew Stacey. Also, you need to use more precise language. If the four circles are allowed to be coincident (to lie on top of each other), then the maximum radius is half the length of the square's side. – Joel Reyes Noche Jan 8 '12 at 0:40
up vote 6 down vote accepted

See the links below. The solutions have been show to be optimal up to 20 circles into a square.

A fun site about all kinds of packing results is:

share|cite|improve this answer
Thank you very much. For 4 circles the answer turns out to be boringly simple, the diameter is just half the length of the side. I was expecting that there existed some hexagonal packing more optimal than this when I asked the questing. – hlovdal May 9 '10 at 20:27

Here are some additional formulas/numbers about circle distances:

share|cite|improve this answer

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.