Geometry problem for the mathletes (not a joke this time)

[pokerfan]

I like to call this the irrigation problem. You have a section of land (one mile square). Or maybe it's cutting identical circles from a square pf cloth or plywood.

Anyway, what is the diameter of the largest circles in each of the following arrangements:



The solutions for n=1 and n=4 are trivial. The n=2 configuration has been posted here before.

[Duer 157099]

1. Huh? I must be a mathtard

I don't even understand the question

[pokerfan]

2. Possilbe I didn't phrase it the best

If the square is 1x1, then what is the diameter of the circles in each of the six pictures.

For one circle, it's obviously 1.
For four circles, it's obviously 0.5.

The others are not so trivial, but answers exist.

[Ptah]

3. I think I've got the three circles in a square.

S=2R+2*sin(75)

if sin(75)=.966 and r=1 then

S=3.932*R

R=.254*S

[pokerfan]

4. correct

[pokerfan]

5. ANSWERS

m=1: 1

n=2:

n=3:

n=4: 0.5

n=5:

n=6:

[Ptah]

6. ?

4/(4+SQRT(2)+SQRT(6))=.508


Edit. I was thinking radius, you answered with diameter.

:blush:

[pokerfan]

7. Complete article

http://mathworld.wolfram.com/CirclePacking.html

http://en.wikipedia.org/wiki/Sphere_packing#Circle_packing