how to position 12 circles evenly in a big circle

Question

This is a realistic question in my study design needed to be solved. Please help.

In a 3-cm² big circle (area=3-cm², so calculated radius of this big circle=9.77 mm), I need to put 12 small holes (all of same dimension). They should be evenly distributed with 4mm spacing from each other, and should be as close to the edge of the big circle as possible. How to position these small holes and how to calculate radius of the small holes?

Thanks

Answer 1

start with placing them at the edge and proceed along a spiral towards the center. their radii depend on whether their proximity to the edge is more important than their size.

Answer 2

Here you have a possible solution based on hexagonal packing:

I am not sure if this satisfies all your requirements, but I guess it will be useful for refining them in case it doesn't represent your problem.

The associated data is:

Hexagon sides -> 4.70882
Circles radii -> 0.35441
Spacing between circles -> 4

Edit/

Another possibility, based on square packing is:

The parameters for the structure are:

Squares side -> 5.65654
Circles radii -> 0.828271
Spacing between circles -> 4

Just to show you that "evenly distributed" is not a good definition: The following solution seems also to cover your requirements:

In this case, the parameters are:

Dodecagon side -> 4.84078
Circles radii -> 0.420388
Spacing between circles -> 4

By the way, the optimal packing for 12 circles is this:

Although they are not evenly distributed.

HTH!